| \[xcycz=0\] |
| \[cxy+cz=0\] |
| \[cx+cyz=0\] |
| has a non-trivial solution, is : |
A) \[\frac{1}{2}\]
B) -1
C) 0
D) 2
Correct Answer: A
Solution :
For non-trivial solution D = 0 \[\left| \begin{matrix} 1 & -c & -c \\ c & -1 & c \\ c & c & -1 \\ \end{matrix} \right|=0\Rightarrow 2{{c}^{3}}-3{{c}^{2}}-1=0\] \[\Rightarrow \]\[{{(c+1)}^{2}}(2c-1)=0\] \[\therefore \]Greatest value of c is \[\frac{1}{2}\]
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