Question

Given matrices \[ A = \begin{bmatrix} 1 & -1 & 4 \\ 3 & 2 & -1 \\ 2 & 1 & -1 \end{bmatrix} \quad\text{and}\quad B = \begin{bmatrix} B_{11} & B_{12} & B_{13} \\ B_{21} & B_{22} & B_{23} \\ B_{31} & B_{32} & B_{33} \end{bmatrix} \] \(B\) is skew-symmetric matrix of \(A\). \(B_{13}\) is?

• A. $-3$
• B. $-2$
• C. $2$
• D. $3$

Hint:

For a skew-symmetric matrix, the elements are related such that $B_{ij} = -B_{ji}$, and the diagonal elements are always zero.

Answer 1

The Correct Option is B

- Since $B$ is the skew-symmetric matrix of $A$, we know that for a skew-symmetric matrix, $B_{ij} = -B_{ji}$. That is, the elements on the diagonal of a skew-symmetric matrix are zero.
- To find $B_{13}$, we use the fact that $B = -A^T$. Hence, \[ B_{13} = -A_{31} = -(2) = -2. \] Thus, the correct answer is (B) $-2$.