If the matrix $\begin{bmatrix} 0 & -1 & 3x \\ 1 & y & -5 \\ -6 & 5 & 0 \end{bmatrix}$ is skew symmetric, then the value of $x+y$ is

If $A = \begin{bmatrix} 4 & -1 & \lambda \\ 2 & 0 & 6 \\ 1 & -2 & 7 \end{bmatrix}$, then $\frac{1}{2}A^{-1}$ exist if

If $\begin{vmatrix} 2 & 3 & 2 \\ x & x & x \\ 4 & 9 & 1 \end{vmatrix} + \begin{vmatrix} 3 & 2 \\ 4 & 5 \end{vmatrix} = 0$, then the value of $x$ is

If $A = \begin{bmatrix} x+z & 2 & -3 \\ x & 0 & 4 \\ 3 & x-y & 0 \end{bmatrix}$ is a skew-symmetric matrix, then which of the following are true?

(A) $y > z > x$

(B) $x > y$

(C) $x + y + z > 0$

(D) $z > x$

Choose the correct answer from the options given below:

If the matrix $\begin{bmatrix}2 & -1 & 3\\ \lambda & 0 & 7\\-1 & 1 & 4\end{bmatrix}$ is not invertible, then value of $\lambda$ is

Assume $P$, $Q$, $R$ and $S$ are matrices of order $2 \times m$, $k \times n$, $m \times 2$ and $2 \times 3$ respectively. The restrictions on $k$, $m$ and $n$, so that $PQ + RS$ is defined are

If $x = \begin{vmatrix}1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2\end{vmatrix}$ then value of $9-2x$ is :