-
question_answer1)
Inverse of the matrix \[\left[ \begin{matrix} 3 & -2 & -1 \\ -4 & 1 & -1 \\ 2 & 0 & 1 \\ \end{matrix} \right]\] is [MP PET 1990]
A)
\[\left[ \begin{matrix} 1 & 2 & 3 \\ 3 & 3 & 7 \\ -2 & -4 & -5 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 1 & -3 & 5 \\ 7 & 4 & 6 \\ 4 & 2 & 7 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 1 & 2 & 3 \\ 2 & 5 & 7 \\ -2 & -4 & -5 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 1 & -3 & 5 \\ 7 & 4 & 6 \\ 4 & 2 & -7 \\ \end{matrix} \right]\] done
clear
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question_answer2)
If A and B are non-singular matrices, then [MP PET 1991; Kurukshetra CEE 1998]
A)
\[{{(AB)}^{-1}}={{A}^{-1}}{{B}^{-1}}\] done
clear
B)
\[AB=BA\] done
clear
C)
\[(AB{)}'={A}'{B}'\] done
clear
D)
\[{{(AB)}^{-1}}={{B}^{-1}}{{A}^{-1}}\] done
clear
View Solution play_arrow
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question_answer3)
Adjoint of the matrix \[N=\left[ \begin{matrix} -4 & -3 & -3 \\ 1 & 0 & 1 \\ 4 & 4 & 3 \\ \end{matrix} \right]\]is [MP PET 1989]
A)
N done
clear
B)
2N done
clear
C)
- N done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer4)
From the following find the correct relation [MP PET 1990]
A)
\[(AB{)}'={A}'{B}'\] done
clear
B)
\[(AB{)}'={B}'{A}'\] done
clear
C)
\[{{A}^{-1}}=\frac{adj\,A}{A}\] done
clear
D)
\[{{(AB)}^{-1}}={{A}^{-1}}{{B}^{-1}}\] done
clear
View Solution play_arrow
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question_answer5)
If A is involutory matrix and I is unit matrix of same order, then \[(I-A)(I+A)\] is
A)
Zero matrix done
clear
B)
A done
clear
C)
I done
clear
D)
2A done
clear
View Solution play_arrow
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question_answer6)
If k is a scalar and I is a unit matrix of order 3, then \[adj(k\,I)=\] [MP PET 1991; Pb. CET 2003]
A)
\[{{k}^{3}}I\] done
clear
B)
\[{{k}^{2}}I\] done
clear
C)
\[-{{k}^{3}}I\] done
clear
D)
\[-{{k}^{2}}I\] done
clear
View Solution play_arrow
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question_answer7)
If A is a \[n\times n\]matrix, then adj(adj A)=
A)
\[|A|{{\,}^{n-1}}A\] done
clear
B)
\[|A|{{\,}^{n-2}}A\] done
clear
C)
\[|A{{|}^{n}}n\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer8)
If \[A=\left[ \begin{matrix} i & 0 \\ 0 & i/2 \\ \end{matrix} \right]\]\[(i=\sqrt{-1}),\]then \[{{A}^{-1}}\]= [MP PET 1992]
A)
\[\left[ \begin{matrix} i & 0 \\ 0 & i/2 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} -i & 0 \\ 0 & -2i \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} i & 0 \\ 0 & 2i \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 0 & i \\ 2i & 0 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer9)
If A is a non- singular matrix, then A(adj A) =
A)
A done
clear
B)
I done
clear
C)
|A|I done
clear
D)
\[|A{{|}^{2}}I\] done
clear
View Solution play_arrow
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question_answer10)
The element of second row and third column in the inverse of \[\left[ \begin{matrix} 1 & 2 & 1 \\ 2 & 1 & 0 \\ -1 & 0 & 1 \\ \end{matrix} \right]\] is [MP PET 1992]
A)
- 2 done
clear
B)
- 1 done
clear
C)
1 done
clear
D)
2 done
clear
View Solution play_arrow
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question_answer11)
If \[R(t)=\left[ \begin{matrix} \cos t & \sin t \\ -\sin t & \cos t \\ \end{matrix} \right],\]then \[R(s).\,R(t)=\] [Roorkee 1981]
A)
\[R(s)+R(t)\] done
clear
B)
\[R\,(st)\] done
clear
C)
\[R(s+t)\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer12)
If A and B be symmetric matrices of the same order, then \[AB-BA\] will be a
A)
Symmetric matrix done
clear
B)
Skew symmetric matrix done
clear
C)
Null matrix done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer13)
If A is a symmetric matrix, then matrix \[{M}'AM\]is [MP PET 1990]
A)
Symmetric done
clear
B)
Skew-symmetric done
clear
C)
Hermitian done
clear
D)
Skew-Hermitian done
clear
View Solution play_arrow
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question_answer14)
An orthogonal matrix is
A)
\[\left[ \begin{matrix} \cos \alpha & 2\sin \alpha \\ -2\sin \alpha & \cos \alpha \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} \cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} \cos \alpha & \sin \alpha \\ \sin \alpha & \cos \alpha \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 1 & 1 \\ 1 & 1 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer15)
If \[A=\left[ \begin{matrix} a & c \\ d & b \\ \end{matrix} \right],\]then \[{{A}^{-1}}\]= [MP PET 1988]
A)
\[\frac{1}{ab-cd}\left[ \begin{matrix} b & -c \\ -d & a \\ \end{matrix} \right]\] done
clear
B)
\[\frac{1}{ad-bc}\left[ \begin{matrix} b & -c \\ -d & a \\ \end{matrix} \right]\] done
clear
C)
\[\frac{1}{ab-cd}\left[ \begin{matrix} b & d \\ c & a \\ \end{matrix} \right]\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer16)
The inverse of the matrix \[\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right]\] is [MP PET 1989; Pb. CET 1989, 1993]
A)
\[\left[ \begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer17)
The inverse of \[\left[ \begin{matrix} 2 & -3 \\ -4 & 2 \\ \end{matrix} \right]\]is [MP PET 1993; Pb. CET 2000]
A)
\[\frac{-1}{8}\,\left[ \begin{matrix} 2 & 3 \\ 4 & 2 \\ \end{matrix} \right]\] done
clear
B)
\[\frac{-1}{8}\,\left[ \begin{matrix} 3 & 2 \\ 2 & 4 \\ \end{matrix} \right]\] done
clear
C)
\[\frac{1}{8}\,\left[ \begin{matrix} 2 & 3 \\ 4 & 2 \\ \end{matrix} \right]\] done
clear
D)
\[\frac{1}{8}\,\left[ \begin{matrix} 3 & 2 \\ 2 & 4 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer18)
Let \[A=\left[ \begin{matrix} 1 & 0 & 0 \\ 5 & 2 & 0 \\ -1 & 6 & 1 \\ \end{matrix} \right]\], then the adjoint of A is [MNR 1982]
A)
\[\left[ \begin{matrix} 2 & -5 & 32 \\ 0 & 1 & -6 \\ 0 & 0 & 2 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} -1 & 0 & 0 \\ -5 & -2 & 0 \\ 1 & -6 & 1 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} -1 & 0 & 0 \\ -5 & -2 & 0 \\ 1 & -6 & -1 \\ \end{matrix} \right]\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer19)
If \[A=\left[ \begin{matrix} 3 & 2 \\ 1 & 4 \\ \end{matrix} \right]\], then \[A(adj\,A)=\] [MP PET 1995; RPET 1997]
A)
\[\left[ \begin{matrix} 10 & 0 \\ 0 & 10 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 0 & 10 \\ 10 & 0 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 10 & 1 \\ 1 & 10 \\ \end{matrix} \right]\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer20)
If A is a square matrix, then which of the following matrices is not symmetric
A)
\[A+{A}'\] done
clear
B)
\[A{A}'\] done
clear
C)
\[{A}'A\] done
clear
D)
\[A-{A}'\] done
clear
View Solution play_arrow
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question_answer21)
If \[A=\left[ \begin{matrix} \cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \\ \end{matrix} \right]\] and \[A\,\,adj\]\[A=\left[ \begin{matrix} k & 0 \\ 0 & k \\ \end{matrix} \right],\] then k is equal to [MP PET 1993; Pb. CET 2001]
A)
0 done
clear
B)
1 done
clear
C)
\[\sin \alpha \cos \alpha \] done
clear
D)
\[\cos 2\alpha \] done
clear
View Solution play_arrow
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question_answer22)
If a matrix A is such that \[3{{A}^{3}}+2{{A}^{2}}+5A+I=0,\] then its inverse is
A)
\[-(3{{A}^{2}}+2A+5I)\] done
clear
B)
\[3{{A}^{2}}+2A+5I\] done
clear
C)
\[3{{A}^{2}}-2A-5I\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer23)
If A and B are square matrices of the same order, then [Pb. CET 1992; Roorkee 1995]
A)
\[(AB{)}'={A}'{B}'\] done
clear
B)
\[(AB{)}'={B}'{A}'\] done
clear
C)
\[AB=O;\]If \[|A|\,=0\]or \[|B|\,=0\] done
clear
D)
\[AB=O;\text{If}\,\,A=I\,\,\text{or }B=I\] done
clear
View Solution play_arrow
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question_answer24)
Which of the following (i) Adjoint of a symmetric matrix is symmetric, (ii) Adjoint of a unit matrix is a unit matrix, (iii) \[A(adj\,A)=(adj\,A)\]\[A=\,|A|I\]and (iv) Adjoint of a diagonal matrix is a diagonal matrix, is/are incorrect
A)
(i) done
clear
B)
(ii) done
clear
C)
(iii) and (iv) done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer25)
\[{{\left[ \begin{matrix} 1 & 3 \\ 3 & 10 \\ \end{matrix} \right]}^{-1}}=\] [EAMCET 1994; DCE 1999]
A)
\[\left[ \begin{matrix} 10 & 3 \\ 3 & 1 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 10 & -3 \\ -3 & 1 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 1 & 3 \\ 3 & 10 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} -1 & -3 \\ -3 & -10 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer26)
The inverse of a symmetric matrix is
A)
Symmetric done
clear
B)
Skew symmetric done
clear
C)
Diagonal matrix done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer27)
If A is a symmetric matrix and \[n\in N\], then \[{{A}^{n}}\]is
A)
Symmetric done
clear
B)
Skew symmetric done
clear
C)
A Diagonal matrix done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer28)
If A is a skew symmetric matrix and n is a positive integer, then \[{{A}^{n}}\]is
A)
A symmetric matrix done
clear
B)
Skew-symmetric matrix done
clear
C)
Diagonal matrix done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer29)
\[{{\left[ \begin{matrix} -6 & 5 \\ -7 & 6 \\ \end{matrix} \right]}^{-1}}\]= [Karnataka CET 1994]
A)
\[\left[ \begin{matrix} -6 & 5 \\ -7 & 6 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 6 & -5 \\ -7 & 6 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 6 & 5 \\ 7 & 6 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 6 & -5 \\ 7 & -6 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer30)
The adjoint of \[\left[ \begin{matrix} 1 & 1 & 1 \\ 1 & 2 & -3 \\ 2 & -1 & 3 \\ \end{matrix} \right]\]is [RPET 1993]
A)
\[\left[ \begin{matrix} 3 & -9 & -5 \\ -4 & 1 & 3 \\ -5 & 4 & 1 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 3 & -4 & -5 \\ -9 & 1 & 4 \\ -5 & 3 & 1 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} -3 & \,\,4 & 5 \\ 9 & -1 & -4 \\ 5 & -3 & -1 \\ \end{matrix} \right]\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer31)
If \[A=\left[ \begin{matrix} 5 & 2 \\ 3 & 1 \\ \end{matrix} \right],\]then \[{{A}^{-1}}\]= [EAMCET 1988]
A)
\[\left[ \begin{matrix} 1 & -2 \\ -3 & 5 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} -1 & 2 \\ 3 & -5 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} -1 & -2 \\ -3 & -5 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 1 & 2 \\ 3 & 5 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer32)
If \[A=\left[ \begin{matrix} 4 & x+2 \\ 2x-3 & x+1 \\ \end{matrix} \right]\]is symmetric, then x = [Karnataka CET 1994]
A)
3 done
clear
B)
5 done
clear
C)
2 done
clear
D)
4 done
clear
View Solution play_arrow
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question_answer33)
The inverse of the matrix \[\left[ \begin{matrix} 3 & -2 \\ 1 & 4 \\ \end{matrix} \right]\]is [MP PET 1994]
A)
\[\left[ \begin{matrix} \frac{4}{14} & \frac{2}{14} \\ \frac{-1}{14} & \frac{3}{14} \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} \frac{3}{14} & \frac{-2}{14} \\ \frac{1}{14} & \frac{4}{14} \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} \frac{4}{14} & \frac{-2}{14} \\ \frac{1}{14} & \frac{3}{14} \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} \frac{3}{14} & \frac{2}{14} \\ \frac{1}{14} & \frac{4}{14} \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer34)
Matrix \[\left[ \begin{matrix} 0 & -4 & 1 \\ 4 & 0 & -5 \\ -1 & 5 & 0 \\ \end{matrix} \right]\]is
A)
Orthogonal done
clear
B)
Idempotent done
clear
C)
Skew- symmetric done
clear
D)
Symmetric done
clear
View Solution play_arrow
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question_answer35)
If \[A=\left[ \begin{matrix} 1 & -2 \\ 5 & 3 \\ \end{matrix} \right]\], then \[A+{{A}^{T}}\]equals [RPET 1994]
A)
\[\left[ \begin{matrix} 2 & 3 \\ 3 & 6 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 2 & -4 \\ 10 & 6 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 2 & 4 \\ -10 & 6 \\ \end{matrix} \right]\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer36)
The inverse of matrix \[A=\left[ \begin{matrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right]\]is [Karnataka CET 1993]
A)
A done
clear
B)
\[{{A}^{T}}\] done
clear
C)
\[\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 1 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer37)
If A is a singular matrix, then adj A is [Karnataka CET 1993]
A)
Singular done
clear
B)
Non-singular done
clear
C)
Symmetric done
clear
D)
Not defined done
clear
View Solution play_arrow
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question_answer38)
The inverse of \[\left[ \begin{matrix} 1 & 2 & 3 \\ 0 & 1 & 2 \\ 0 & 0 & 1 \\ \end{matrix} \right]\]is [EAMCET 1990]
A)
\[\left[ \begin{matrix} 1 & -2 & 1 \\ 0 & 1 & -2 \\ 0 & 0 & 0 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 1 & -2 & 1 \\ 0 & 1 & -2 \\ 0 & 0 & 1 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 1 & 2 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 1 \\ \end{matrix} \right]\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer39)
Which one of the following statements is true [MP PET 1996]
A)
Non- singular square matrix does not have a unique inverse done
clear
B)
Determinant of a non-singular matrix is zero done
clear
C)
If \[{A}'=A,\]then A is a square matrix done
clear
D)
If \[|A|\,\ne 0\], then \[|A.adj\,A|\,=\,|A{{|}^{(n-1)}}\], where \[A={{[{{a}_{ij}}]}_{n\times n}}\] done
clear
View Solution play_arrow
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question_answer40)
If matrix \[A=\left[ \begin{matrix} 1 & -1 \\ 1 & 1 \\ \end{matrix} \right],\]then [MP PET 1996]
A)
\[{A}'=\left[ \begin{matrix} 1 & \,\,1 \\ 1 & -1 \\ \end{matrix} \right]\] done
clear
B)
\[{{A}^{-1}}=\left[ \begin{matrix} \,\,1 & 1 \\ -1 & 1 \\ \end{matrix} \right]\] done
clear
C)
\[A.\,\,\left[ \begin{matrix} \,\,1 & 1 \\ -1 & 1 \\ \end{matrix} \right]=2I\] done
clear
D)
\[\lambda A=\left[ \begin{matrix} \lambda & -\lambda \\ 1 & -1 \\ \end{matrix} \right]\]where \[\lambda \]is a non zero scalar done
clear
View Solution play_arrow
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question_answer41)
Which of the following is not true [Kurukshetra CEE 1996]
A)
Every skew-symmetric matrix of odd order is non-singular done
clear
B)
If determinant of a square matrix is non-zero, then it is non singular done
clear
C)
Adjoint of symmetric matrix is symmetric done
clear
D)
Adjoint of a diagonal matrix is diagonal done
clear
View Solution play_arrow
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question_answer42)
If \[A=\left( \begin{matrix} 1 & 2 & 0 \\ 0 & 1 & 2 \\ 2 & 0 & 1 \\ \end{matrix} \right),\]then adj A [RPET 1996]
A)
\[\left( \begin{matrix} 1 & 4 & -2 \\ -2 & 1 & 4 \\ 4 & -2 & 1 \\ \end{matrix} \right)\] done
clear
B)
\[\left( \begin{matrix} 1 & -2 & 4 \\ 4 & 1 & -2 \\ -2 & 4 & 1 \\ \end{matrix} \right)\] done
clear
C)
\[\left( \begin{matrix} 1 & 2 & 4 \\ -4 & 1 & 2 \\ -4 & -2 & 1 \\ \end{matrix} \right)\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer43)
Which one of the following is correct [Kurukshetra CEE 1998]
A)
Skew- symmetric matrix of odd order is non-singular done
clear
B)
Skew-symmetric matrix of odd order is singular done
clear
C)
Skew-symmetric matrix of even order is always singular done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer44)
\[Adj.\]\[(AB)-(Adj.\,B)(Adj.\,A)=\] [MP PET 1997]
A)
\[Adj.A-Adj\,B\] done
clear
B)
I done
clear
C)
O done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer45)
If \[A=\left( \begin{matrix} 3 & 2 \\ 0 & 1 \\ \end{matrix} \right)\], then \[{{({{A}^{-1}})}^{3}}\]is equal to [MP PET 1997; Pb. CET 2003]
A)
\[\frac{1}{27}\left( \begin{matrix} 1 & -26 \\ 0 & 27 \\ \end{matrix} \right)\] done
clear
B)
\[\frac{1}{27}\left( \begin{matrix} -1 & 26 \\ 0 & 27 \\ \end{matrix} \right)\] done
clear
C)
\[\frac{1}{27}\left( \begin{matrix} 1 & -26 \\ 0 & -27 \\ \end{matrix} \right)\] done
clear
D)
\[\frac{1}{27}\left( \begin{matrix} -1 & -26 \\ 0 & -27 \\ \end{matrix} \right)\] done
clear
View Solution play_arrow
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question_answer46)
The matrix \[\left( \begin{matrix} 1 & a & 2 \\ 1 & 2 & 5 \\ 2 & 1 & 1 \\ \end{matrix} \right)\]is not invertible, if ?a? has the value [MP PET 1998]
A)
2 done
clear
B)
1 done
clear
C)
0 done
clear
D)
-1 done
clear
View Solution play_arrow
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question_answer47)
For any \[2\times 2\] matrix A, if \[A(adj.\,\,A)\]= \[\left[ \begin{matrix} 10 & 0 \\ 0 & 10 \\ \end{matrix} \right]\], then \[|A|\,=\] [MP PET 1999]
A)
0 done
clear
B)
10 done
clear
C)
20 done
clear
D)
100 done
clear
View Solution play_arrow
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question_answer48)
If A is a square matrix for which \[{{a}_{ij}}={{i}^{2}}-{{j}^{2}}\], then A is [RPET 1999]
A)
Zero matrix done
clear
B)
Unit matrix done
clear
C)
Symmetric matrix done
clear
D)
Skew symmetric matrix done
clear
View Solution play_arrow
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question_answer49)
Inverse matrix of \[\left[ \begin{matrix} 4 & 7 \\ 1 & 2 \\ \end{matrix} \right]\] [RPET 1996, 2001]
A)
\[\left[ \begin{matrix} 2 & -7 \\ -1 & 4 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 2 & -1 \\ -7 & 4 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} -2 & 7 \\ 1 & -4 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} -2 & 1 \\ 7 & -4 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer50)
If \[A=\left[ \begin{matrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \\ \end{matrix} \right]\], then \[{{A}^{-1}}\]= [DCE 1999]
A)
A done
clear
B)
\[{{A}^{2}}\] done
clear
C)
\[{{A}^{3}}\] done
clear
D)
\[{{A}^{4}}\] done
clear
View Solution play_arrow
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question_answer51)
If d is the determinant of a square matrix A of order n, then the determinant of its adjoint is [EAMCET 2000]
A)
\[{{d}^{n}}\] done
clear
B)
\[{{d}^{n-1}}\] done
clear
C)
\[{{d}^{n+1}}\] done
clear
D)
\[d\] done
clear
View Solution play_arrow
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question_answer52)
If A and B are non-singular square matrices of same order, then \[adj(AB)\]is equal to [AMU 1999]
A)
\[(adj\,A)(adj\,B)\] done
clear
B)
\[(adj\,B)(adj\,A)\] done
clear
C)
\[(adj\,{{B}^{-1}})(adj\,{{A}^{-1}})\] done
clear
D)
\[(adj\,{{A}^{-1}})(adj\,{{B}^{-1}})\] done
clear
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question_answer53)
The element in the first row and third column of the inverse of the matrix \[\left[ \begin{matrix} 1 & 2 & -3 \\ 0 & 1 & 2 \\ 0 & 0 & 1 \\ \end{matrix} \right]\]is [MP PET 2000]
A)
- 2 done
clear
B)
0 done
clear
C)
1 done
clear
D)
7 done
clear
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question_answer54)
For any square matrix A, \[A{{A}^{T}}\]is a [RPET 2000]
A)
Unit matrix done
clear
B)
Symmetric matrix done
clear
C)
Skew symmetric matrix done
clear
D)
Diagonal matrix done
clear
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question_answer55)
The matrix \[\left[ \begin{matrix} \lambda & -1 & 4 \\ -3 & 0 & 1 \\ -1 & 1 & 2 \\ \end{matrix} \right]\]is invertible, if [Kurukshetra CEE 1996]
A)
\[\lambda \ne -15\] done
clear
B)
\[\lambda \ne -17\] done
clear
C)
\[\lambda \ne -16\] done
clear
D)
\[\lambda \ne -18\] done
clear
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question_answer56)
For a matrix A, AI = A and \[A{{A}^{T}}=I\]is true for [RPET 2000]
A)
If A is a square matrix done
clear
B)
If A is a non singular matrix done
clear
C)
If A is a symmetric matrix done
clear
D)
If A is any matrix done
clear
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question_answer57)
If \[{{I}_{3}}\] is the identity matrix of order 3, then \[I_{3}^{-1}\]is [Pb. CET 2000]
A)
0 done
clear
B)
\[3{{I}_{3}}\] done
clear
C)
\[{{I}_{3}}\] done
clear
D)
Does not exist done
clear
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question_answer58)
The matrix \[\left[ \begin{matrix} 0 & 5 & -7 \\ -5 & 0 & 11 \\ 7 & -11 & 0 \\ \end{matrix} \right]\]is known as [Karnataka CET 2000]
A)
Upper triangular matrix done
clear
B)
Skew symmetric matrix done
clear
C)
Symmetric matrix done
clear
D)
Diagonal matrix done
clear
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question_answer59)
If \[A=\left( \begin{matrix} 1 & -2 & 1 \\ 2 & 1 & 3 \\ \end{matrix} \right)\]and \[B=\left( \begin{matrix} 2 & 1 \\ 3 & 2 \\ 1 & 1 \\ \end{matrix} \right)\], then \[{{(AB)}^{T}}\]is equal to [RPET 2001]
A)
\[\left( \begin{matrix} -3 & -2 \\ 10 & 7 \\ \end{matrix} \right)\] done
clear
B)
\[\left( \begin{matrix} -3 & 10 \\ -2 & 7 \\ \end{matrix} \right)\] done
clear
C)
\[\left( \begin{matrix} -3 & 7 \\ 10 & 2 \\ \end{matrix} \right)\] done
clear
D)
None of these done
clear
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question_answer60)
If \[A=\left[ \begin{matrix} 1 & -1 \\ 2 & 3 \\ \end{matrix} \right]\], then adj A is equal to [RPET 2001]
A)
\[\left[ \begin{matrix} -3 & -1 \\ 2 & -1 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 3 & 1 \\ -2 & 1 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 3 & -2 \\ 1 & 1 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} \,3 & -1 \\ -2 & 1 \\ \end{matrix} \right]\] done
clear
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question_answer61)
If A is a square matrix, then \[A+{{A}^{T}}\]is [RPET 2001]
A)
Non singular matrix done
clear
B)
Symmetric matrix done
clear
C)
Skew-symmetric matrix done
clear
D)
Unit matrix done
clear
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question_answer62)
The inverse of a matrix \[A=\left( \begin{matrix} a & b \\ c & d \\ \end{matrix} \right)\]is [AMU 2001]
A)
\[\left( \begin{matrix} d & -b \\ -c & a \\ \end{matrix} \right)\] done
clear
B)
\[\frac{1}{(ad-bc)}\left( \begin{matrix} d & -b \\ -c & a \\ \end{matrix} \right)\] done
clear
C)
\[\frac{1}{|A|}\left( \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right)\] done
clear
D)
\[\left( \begin{matrix} b & -a \\ d & -c \\ \end{matrix} \right)\] done
clear
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question_answer63)
If \[A=\left[ \begin{matrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \\ \end{matrix} \right]\], then which of the following statements is not correct [DCE 2001]
A)
A is orthogonal matrix done
clear
B)
\[{A}'\]is orthogonal matrix done
clear
C)
Determinant A = 1 done
clear
D)
A is not invertible done
clear
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question_answer64)
If \[{{A}^{2}}-A+I=0\], then \[{{A}^{-1}}\]= [Kerala (Engg,) 2001; AIEEE 2005]
A)
\[{{A}^{-2}}\] done
clear
B)
\[A+I\] done
clear
C)
\[I-A\] done
clear
D)
\[A-I\] done
clear
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question_answer65)
If \[A=\left[ \begin{matrix} 2 & 2 \\ -3 & 2 \\ \end{matrix} \right]\] and \[B=\left[ \begin{matrix} 0 & -1 \\ 1 & 0 \\ \end{matrix} \right],\] then \[{{({{B}^{-1}}{{A}^{-1}})}^{-1}}\]= [EAMCET 2001]
A)
\[\left[ \begin{matrix} 2 & -2 \\ 2 & 3 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 3 & -2 \\ 2 & 2 \\ \end{matrix} \right]\] done
clear
C)
\[\frac{1}{10}\left[ \begin{matrix} 2 & 2 \\ -2 & 3 \\ \end{matrix} \right]\] done
clear
D)
\[\frac{1}{10}\left[ \begin{matrix} 3 & 2 \\ -2 & 2 \\ \end{matrix} \right]\] done
clear
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question_answer66)
A square matrix \[A=[{{a}_{ij}}]\] in which \[{{a}_{ij}}=0\] for \[i\,\ne j\] and \[{{a}_{ij}}=k\] (constant) for \[i=j\] is called a [EAMCET 2001]
A)
Unit matrix done
clear
B)
Scalar matrix done
clear
C)
Null matrix done
clear
D)
Diagonal matrix done
clear
View Solution play_arrow
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question_answer67)
For two invertible matrices A and B of suitable orders, the value of \[{{(AB)}^{-1}}\]is [Pb. CET 2000, RPET 2000, 02; Karnataka CET 2001]
A)
\[{{(BA)}^{-1}}\] done
clear
B)
\[{{B}^{-1}}{{A}^{-1}}\] done
clear
C)
\[{{A}^{-1}}{{B}^{-1}}\] done
clear
D)
\[{{(A{B}')}^{-1}}\] done
clear
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question_answer68)
If \[A=\left[ \begin{matrix} -1 & 2 \\ 2 & -1 \\ \end{matrix} \right]\]and \[B=\left[ \begin{align} & 3 \\ & 1 \\ \end{align} \right],AX=B\], then \[X=\] [MP PET 2002]
A)
[5 7] done
clear
B)
\[\frac{1}{3}\left[ \begin{align} & 5 \\ & 7 \\ \end{align} \right]\] done
clear
C)
\[\frac{1}{3}[5\,\,7]\] done
clear
D)
\[\left[ \begin{align} & 5 \\ & 7 \\ \end{align} \right]\] done
clear
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question_answer69)
If \[A=\left[ \begin{matrix} 1 & 2 \\ 3 & -5 \\ \end{matrix} \right]\], then \[{{A}^{-1}}\]= [MP PET 2002]
A)
\[\left[ \begin{matrix} -5 & -2 \\ -3 & 1 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} \frac{5}{11} & \frac{2}{11} \\ \frac{3}{11} & -\frac{1}{11} \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} -\frac{5}{11} & -\frac{2}{11} \\ -\frac{3}{11} & -\frac{1}{11} \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 5 & 2 \\ 3 & -1 \\ \end{matrix} \right]\] done
clear
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question_answer70)
If \[A=\left[ \begin{matrix} 2 & 3 \\ 4 & 6 \\ \end{matrix} \right]\], then \[{{A}^{-1}}\]= [Karnataka CET 2001]
A)
\[\left[ \begin{matrix} 1 & 2 \\ -3/2 & 3 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 2 & -3 \\ 4 & 6 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} -2 & 4 \\ -3 & 6 \\ \end{matrix} \right]\] done
clear
D)
Does not exist done
clear
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question_answer71)
If \[A=\left[ \begin{matrix} 4 & 2 \\ 3 & 4 \\ \end{matrix} \right]\],then \[|adj\,\,A|\]is equal to [UPSEAT 2003]
A)
16 done
clear
B)
10 done
clear
C)
6 done
clear
D)
None of these done
clear
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question_answer72)
The matrix \[A=\left[ \begin{matrix} 1 & -3 & -4 \\ -1 & \,\,\,3 & \,\,4 \\ 1 & -3 & -4 \\ \end{matrix} \right]\] is nilpotent of index [Kurukshetra CEE 2002]
A)
2 done
clear
B)
3 done
clear
C)
4 done
clear
D)
6 done
clear
View Solution play_arrow
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question_answer73)
The matrix \[A=\left[ \begin{matrix} i & 1-2i \\ -1-2i & 0 \\ \end{matrix} \right]\]is which of the following [Kurukshetra CEE 2002]
A)
Symmetric done
clear
B)
Skew-symmetric done
clear
C)
Hermitian done
clear
D)
Skew-hermitian done
clear
View Solution play_arrow
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question_answer74)
The adjoint matrix of \[\left[ \begin{matrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \\ \end{matrix} \right]\]is [MP PET 2003]
A)
\[\left[ \begin{matrix} 4 & 8 & 3 \\ 2 & 1 & 6 \\ 0 & 2 & 1 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 1 & -1 & 0 \\ -2 & 3 & -4 \\ -2 & 3 & -3 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 11 & 9 & 3 \\ 1 & 2 & 8 \\ 6 & 9 & 1 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 1 & -2 & 1 \\ -1 & 3 & 3 \\ -2 & 3 & -3 \\ \end{matrix} \right]\] done
clear
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question_answer75)
\[A=\left[ \begin{matrix} 0 & 3 \\ 2 & 0 \\ \end{matrix} \right]\]and \[{{A}^{-1}}=\lambda (adj(A)),\]then \[\lambda =\] [UPSEAT 2002]
A)
\[\frac{-1}{6}\] done
clear
B)
\[\frac{1}{3}\] done
clear
C)
\[\frac{-1}{3}\] done
clear
D)
\[\frac{1}{6}\] done
clear
View Solution play_arrow
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question_answer76)
Which of the following is true for matrix \[AB\] [RPET 2003]
A)
\[{{(AB)}^{-1}}={{A}^{-1}}{{B}^{-1}}\] done
clear
B)
\[{{(AB)}^{-1}}={{B}^{-1}}{{A}^{-1}}\] done
clear
C)
\[AB=BA\] done
clear
D)
All of these done
clear
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question_answer77)
If \[A=\left[ \begin{matrix} \cos x & \sin x \\ -\sin x & \cos x \\ \end{matrix} \right]\], then \[A.\]\[(adj(A))\]= [RPET 2003]
A)
\[\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 1 & 1 \\ 0 & 0 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} -2 & 0 \\ 0 & -2 \\ \end{matrix} \right]\] done
clear
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question_answer78)
The inverse matrix of \[\left[ \begin{matrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \\ \end{matrix} \right],\]is [MP PET 2003]
A)
\[\left[ \begin{matrix} \frac{1}{2} & -\frac{1}{2} & \frac{1}{2} \\ -4 & 3 & -1 \\ \frac{5}{2} & \frac{-3}{2} & \frac{1}{2} \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} \frac{1}{2} & -4 & \frac{5}{2} \\ 1 & -6 & 3 \\ 1 & 2 & -1 \\ \end{matrix} \right]\] done
clear
C)
\[\frac{1}{2}\left[ \begin{matrix} 1 & 2 & 3 \\ 3 & 2 & 1 \\ 4 & 2 & 3 \\ \end{matrix} \right]\] done
clear
D)
\[\frac{1}{2}\left[ \begin{matrix} 1 & -1 & -1 \\ -8 & 6 & -2 \\ 5 & -3 & 1 \\ \end{matrix} \right]\] done
clear
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question_answer79)
The multiplicative inverse of matrix \[\left[ \begin{matrix} 2 & 1 \\ 7 & 4 \\ \end{matrix} \right]\]is [DCE 2002]
A)
\[\left[ \begin{matrix} 4 & -1 \\ -7 & -2 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} -4 & -1 \\ 7 & -2 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 4 & -7 \\ 7 & 2 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 4 & -1 \\ -7 & 2 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer80)
If \[A=\left[ \begin{matrix} -2 & 6 \\ -5 & 7 \\ \end{matrix} \right]\], then adj [UPSEAT 2002]
A)
\[\left[ \begin{matrix} 7 & -6 \\ 5 & -2 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 2 & -6 \\ 5 & -7 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 7 & -5 \\ 6 & -2 \\ \end{matrix} \right]\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer81)
If matrix \[A=\left[ \begin{matrix} 3 & 2 & 4 \\ 1 & 2 & -1 \\ 0 & 1 & 1 \\ \end{matrix} \right]\]and \[{{A}^{-1}}=\frac{1}{K}adj(A),\] then \[K\]is [UPSEAT 2002]
A)
7 done
clear
B)
-7 done
clear
C)
\[\frac{1}{7}\] done
clear
D)
11 done
clear
View Solution play_arrow
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question_answer82)
If \[A=\left[ \begin{matrix} 3 & 4 \\ 5 & 7 \\ \end{matrix} \right]\], then \[A\,(adj\,A)\]= [RPET 2002]
A)
I done
clear
B)
|A| done
clear
C)
\[|A|I\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer83)
If for the matrix A, \[{{A}^{3}}=I\], then \[{{A}^{-1}}=\] [RPET 2002]
A)
\[{{A}^{2}}\] done
clear
B)
\[{{A}^{3}}\] done
clear
C)
A done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer84)
If \[A=\left[ \begin{matrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \\ \end{matrix} \right],\]then \[{{A}^{-1}}=\] [MP PET 2004]
A)
I done
clear
B)
- I done
clear
C)
- A done
clear
D)
A done
clear
View Solution play_arrow
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question_answer85)
Inverse of the matrix \[\left( \begin{matrix} 1 & -2 \\ 3 & 4 \\ \end{matrix} \right)\] is [Karnataka CET 2003]
A)
\[\frac{1}{10}\left( \begin{matrix} 4 & 2 \\ -3 & 1 \\ \end{matrix} \right)\] done
clear
B)
\[\frac{1}{10}\left( \begin{matrix} 1 & -2 \\ 3 & 4 \\ \end{matrix} \right)\] done
clear
C)
\[\frac{1}{10}\left( \begin{matrix} 4 & 2 \\ -3 & 1 \\ \end{matrix} \right)\] done
clear
D)
\[\left( \begin{matrix} 4 & 2 \\ -3 & 1 \\ \end{matrix} \right)\] done
clear
View Solution play_arrow
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question_answer86)
Inverse of the matrix \[\left[ \begin{matrix} \cos 2\theta & -\sin 2\theta \\ \sin 2\theta & \cos 2\theta \\ \end{matrix} \right]\]is [Karnataka CET 2004]
A)
\[\left[ \begin{matrix} \cos 2\theta & -\sin 2\theta \\ \sin 2\theta & \cos 2\theta \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} \cos 2\theta & \sin 2\theta \\ \sin 2\theta & -\cos 2\theta \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} \cos 2\theta & \sin 2\theta \\ \sin 2\theta & \cos 2\theta \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} \cos 2\theta & \sin 2\theta \\ -\sin 2\theta & \cos 2\theta \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer87)
Let \[A=\left( \begin{matrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \\ \end{matrix} \right)\] and \[(10)B=\left( \begin{matrix} 4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \\ \end{matrix} \right)\]. If B is the inverse of matrix A, then \[\alpha \]is [AIEEE 2004]
A)
5 done
clear
B)
- 1 done
clear
C)
2 done
clear
D)
- 2 done
clear
View Solution play_arrow
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question_answer88)
For any \[2\times 2\] matrix A, if \[A(adj\,A)=\left[ \begin{matrix} 10 & 0 \\ 0 & 10 \\ \end{matrix} \right]\] then \[|A|\] is equal [Pb. CET 2002]
A)
0 done
clear
B)
10 done
clear
C)
20 done
clear
D)
100 done
clear
View Solution play_arrow
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question_answer89)
If \[A,B,C\]are three \[n\times n\]matrices, then \[(ABC{)}'=\] [MP PET 1988]
A)
\[{A}'\,{B}'\,{C}'\] done
clear
B)
\[{C}'\,{B}'\,{A}'\] done
clear
C)
\[{B}'\,{C}'\,{A}'\] done
clear
D)
\[{B}'\,{A}'\,{C}'\] done
clear
View Solution play_arrow
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question_answer90)
If X is a square matrix of order 3 × 3 and \[\lambda \] is a scalar, then adj (\[\lambda X)\] is equal to [J & K 2005]
A)
\[\lambda \,adjX\] done
clear
B)
\[{{\lambda }^{3}}adj\,X\] done
clear
C)
\[{{\lambda }^{2}}adj\,X\] done
clear
D)
\[{{\lambda }^{4}}adj\,X\] done
clear
View Solution play_arrow
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question_answer91)
If \[X=\left[ \begin{matrix} -x & -y \\ z & t \\ \end{matrix} \right]\] then transpose of adj X is [J & K 2005]
A)
\[\left[ \begin{matrix} t & z \\ -y & -x \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} t & y \\ -z & -x \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} t & -z \\ y & -x \\ \end{matrix} \right]\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer92)
The inverse of the matrix \[\left[ \begin{matrix} 5 & -2 \\ 3 & 1 \\ \end{matrix} \right]\] is[Karnataka CET 2005]
A)
\[\frac{1}{11}\left[ \begin{matrix} 1 & 2 \\ -3 & 5 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 1 & 2 \\ -3 & 5 \\ \end{matrix} \right]\] done
clear
C)
\[\frac{1}{13}\left[ \begin{matrix} -2 & 5 \\ 1 & 3 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 1 & 3 \\ -2 & 5 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer93)
\[A=\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 1 \\ 0 & -2 & 4 \\ \end{matrix} \right];\,\,I=\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right]\]\[{{A}^{-1}}=\frac{1}{6}[{{A}^{2}}+cA+dI]\] where \[c,d\in R\], then pair of values \[(c,d)\] [IIT Screening 2005]
A)
(6, 11) done
clear
B)
(6, -11) done
clear
C)
(-6, 11) done
clear
D)
(-6, -11) done
clear
View Solution play_arrow
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question_answer94)
If \[P=\left[ \begin{matrix} \frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2} \\ \end{matrix} \right],\,A=\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \\ \end{matrix} \right]\] and \[Q=PA{{P}^{T}}\], then \[P({{Q}^{2005}}){{P}^{T}}\] equal to [IIT Screening 2005]
A)
\[\left[ \begin{matrix} 1 & 2005 \\ 0 & 1 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} \sqrt{3}/2 & 2005 \\ 1 & 0 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 1 & 2005 \\ \sqrt{3}/2 & 1 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 1 & \sqrt{3}/2 \\ 0 & 2005 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer95)
If \[A=\left[ \begin{matrix} 1 & -1 & 1 \\ 0 & 2 & -3 \\ 2 & 1 & 0 \\ \end{matrix} \right]\] and \[B=(adj\,A)\], and \[C=5A,\] then \[\frac{|adjB|}{|C|}\]= [Kerala (Engg.) 2005]
A)
5 done
clear
B)
25 done
clear
C)
-1 done
clear
D)
1 done
clear
E)
125 done
clear
View Solution play_arrow
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question_answer96)
If A is a unit matrix of order n, then \[A(adj\,A)\]is [DCE 2005]
A)
Zero matrix done
clear
B)
Row matrix done
clear
C)
Unit matrix done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer97)
If A is a skew-symmetric matrix of order n, and C is a column matrix of order \[n\times 1\], then \[{{C}^{T}}\]AC is [AMU 2005]
A)
A Identity matrix of order n done
clear
B)
A unit matrix of order one done
clear
C)
A zero matrix of order one done
clear
D)
None of these done
clear
View Solution play_arrow