A) - 2
B) 2
C) - 4
D) 4
Correct Answer: D
Solution :
\[{{M}^{2}}-\lambda M-{{I}_{2}}=0\] \[\Rightarrow \,\,\left[ \begin{matrix} 1 & 2 \\ 2 & 3 \\ \end{matrix} \right]\left[ \begin{matrix} 1 & 2 \\ 2 & 3 \\ \end{matrix} \right]-\left[ \begin{matrix} \lambda & 2\lambda \\ 2\lambda & 3\lambda \\ \end{matrix} \right]-\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]=O\] \[\Rightarrow \,\,\left[ \begin{matrix} 5 & 8 \\ 8 & 13 \\ \end{matrix} \right]-\left[ \begin{matrix} \lambda & 2\lambda \\ 2\lambda & 3\lambda \\ \end{matrix} \right]-\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]=O\] \[\Rightarrow \,\,\left[ \begin{matrix} 5-\lambda & 8-2\lambda \\ 8-2\lambda & 13-3\lambda \\ \end{matrix} \right]=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] Þ \[5-\lambda =1,\,\,8-2\lambda =0,\,\,13-3\lambda =1\] Þ \[\lambda =4\], which satisfies all the three equations.
You need to login to perform this action.
You will be redirected in
3 sec
