MCQ
If $A = \left[ {\begin{array}{*{20}{c}}1&2&3\\{ - 2}&3&{ - 1}\\3&1&2\end{array}} \right]$and $I $is a unit matrix of ${3^{rd}}$order, then $({A^2} + 9I)$ equals
- A$2A$
- B$4A$
- C$6A$
- ✓None of these
$I = \left[ {\begin{array}{*{20}{c}}1&0&0\\0&1&0\\0&0&1\end{array}} \right]$,then, ${A^2} + 9I = \,\left[ {\begin{array}{*{20}{c}}{15}&{11}&7\\{ - 11}&{13}&{ - 11}\\7&{11}&{21}\end{array}} \right]$.
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$1.$ The number of matrices in $\Omega$ is
$(A)$ $12$ $(B)$ $6$ $(C)$ $9$ $(D)$ $3$
$2.$ The number of matrices $A$ in $\Omega$ for which the system of linear equations
$A\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ has a unique solution, is
$(A)$ less than $4$
$(B)$ at least $4$ but less than $7$
$(C)$ at least $7$ but less than $10$
$(D)$ at least $10$
$3.$ The number of matrices $A$ in $\Omega$ for which the system of linear equations
$A\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ is inconsistent, is
$(A)$ $0$ $(B)$ more than $2$ $(C)$ $2$ $(D)$ $1$