Solve system of linear equations, using matrix method.

$5 x+2 y=3$ $3 x+2 y=5$

Number of value of $'a'$ for which the system of equations,$A^2 x + (2 – a) y = 4 + a^2$ $a x + (2 a – 1) y = a^5 – 2$ possess no solution is

The following system of equation $3x – 2y + z = 0$, $\lambda x – 14y + 15z = 0$, $x + 2y – 3z = 0$ has a solution other than $x = y = z = 0$ for $\lambda $ equal to

If $A$ is matrix such that $A^2 + A + 2I = O$, then which of the following is $INCORRECT$ ?

Let $\Omega$ be the set of all $3 \times 3$ symmetric matrices all of whose entries are either $0$ or $1$ . Five of these entries are $1$ and four of them are $0$ .

$1.$ 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 $2$ $(C)$ $2$ $(D)$ $1$