If the matrix $\begin{bmatrix} -1 & x-y & 4 \\ 2 & 0 & 5 \\ x+y & z & 6 \end{bmatrix}$ is symmetric, then $x + 3y + 2z$ is equal to

The system of equations

$x + y + z = 7$

$x + 2y + 3z = 5$

$x + 3y + \lambda z = \mu$

has a unique solution, if

The matrix $A = \begin{bmatrix}0 & 0 & 5\\0 & 5 & 0\\5 & 0 & 0\end{bmatrix}$ is a

(A) Diagonal matrix

(B) Scalar matrix

(C) Square matrix

(D) Symmetric matrix

Choose the correct answer from the options given below:

If the matrix $\left[\begin{array}{rrr}0 & -1 & 3 x \\ 1 & y & -5 \\ -6 & 5 & 0\end{array}\right]$ is skew-symmetric, then the value of $5 x-y$ is:

If A is a square matrix of order $n$, then

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

If $\begin{bmatrix} a-b & 0 & 0 \\ 0 & b-c & 0 \\ 0 & 0 & c-2 \end{bmatrix}$ is a scalar matrix such that $a + b + c = 0$, then, which of the following are TRUE?

(A) $a = 0$

(B) $b = 0$

(C) $a = 1$

(D) $c = 1$

Choose the correct answer from the options given below:

The system of equations

$x + y + z = 4$

$x + 2y + 3z = 12$

$x + 3y + \lambda z = \mu$ has a unique solution if