A) 1
B) 3
C) 2
D) 0
Correct Answer: C
Solution :
[c] Here to find the value of \[tr(A)-tr(B),\] we need not to find the matrices A and B. We can find tr(A)-tr[b] using the properties of trace of matrix, i.e., \[A+2B=\left[ \begin{matrix} 1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1 \\ \end{matrix} \right]\Rightarrow tr(A+2B)=-1(1)\] Or \[tr(A)+2tr(B)=-1\] \[\Rightarrow 2A-B=\left[ \begin{matrix} 2 & -1 & 5 \\ 2 & -1 & 6 \\ 0 & 1 & 2 \\ \end{matrix} \right]\] \[\Rightarrow tr(2A-B)=3\] or \[2tr(A)-tr(B)=3(2)\] Solving (1) and (2), we get tr[a] = 1 and tr[b] = -1 \[\Rightarrow tr(A)-tr(B)=2\]You need to login to perform this action.
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