If A and B are square matrices of order 3 such that |A| = -1 and |B| = 5, then the value of |3AB| is

If $[1 \quad 2 \quad 1] \begin{bmatrix} -1 & 0 & 1 \\ 1 & 2 & -1 \\ 0 & 1 & 3 \end{bmatrix} \begin{bmatrix} 2x \\ x \\ -7 \end{bmatrix} = [0]$, then the value of $x$ is

If the area of a triangle whose vertices are (-1, 3), (1, -5) and (k, 2) where $k > 0$ is 30 sq. units, then the value of k is

If $\begin{vmatrix}x-2 & 2x-3 & 3x-4\\x-4 & 2x-9 & 3x-16\\x-8 & 2x-27 & 3x-64\end{vmatrix} = 0$ then the value of x is:

If the matrix $M = \begin{bmatrix} 0 & -1 & 3\alpha \\ 1 & \beta & -5 \\ -6 & 5 & 0 \end{bmatrix}$ is skew-symmetric, then

The value(s) of $K$, for which the system of linear equations $2x + y + z = 1, x + Ky - z = \frac{3}{2}$ and $3y - 5z = 9$ does not possess a unique solution is

The system of equations

$x + y + z = 4$

$x + 2y + 3z = 12$

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