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

The Correct Option is C

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 \( 5x - y \):

\[ 5x - y = 5(2) - 0 = 10. \]