If the matrix $A =\begin{bmatrix}x&2&y\\-2&0&3\\-1&z&0\end{bmatrix}$ is skew-symmetric, then the value of $2x-3y+5z$ is equal to
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → -18 **
For a skew-symmetric matrix $A$,
$A^{T}=-A$ and all diagonal elements are $0$.
Given:
$A=\begin{bmatrix} x & 2 & y \\ -2 & 0 & 3 \\ -1 & z & 0 \end{bmatrix}$
Diagonal element condition:
$x=0$
Off–diagonal conditions:
$a_{13}=-a_{31}\Rightarrow y=-(-1)=1$
$a_{23}=-a_{32}\Rightarrow 3=-z\Rightarrow z=-3$
Now compute:
$2x-3y+5z=2(0)-3(1)+5(-3)$
$=-3-15=-18$