Question

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

• A. 12
• B. 15
• C. 10
• D. 14

Answer 1

Answer: (C)

10

Answer 2

A matrix is skew-symmetric if $a_{ij} = -a_{ji}$ and the diagonal elements are zero.

From $a_{13} = 3x$ and $a_{31} = -6$:

$3x = -(-6) \implies 3x = 6 \implies x = 2.$

From $a_{23} = -5$ and $a_{32} = 5$:

$y = -y \implies y = 0.$

Substitute $x = 2$ and $y = 0$ into $5x - y$:

$5x - y = 5(2) - 0 = 10.$