A) 1
B) 2
C) 4
D) No such 'a' exists
Correct Answer: A
Solution :
\[A\,3\times 3\] matrix is equivalent to \[{{I}_{3}}\] if it is non-singular. |
Hence \[\left| \begin{matrix} 1 & 2a & 2 \\ 0 & -1 & 1 \\ a & 1 & 3 \\ \end{matrix} \right|\,\,=0\]\[\Rightarrow \] \[-\,4+a\,(2a+2)=0\]\[\Rightarrow \]\[2{{a}^{2}}+2a-4=0\]\[\Rightarrow \] \[(a+2)\,\,(a-1)=0\to a=-\,2,\,\,1\] |
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