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Question

If the matrix $\begin{bmatrix} 2 & 3 \\ 5 & -1 \end{bmatrix} = A + B$, where $A$ is symmetric and $B$ is skew-symmetric, then $B =$ _______

$\begin{bmatrix} 2 & 4 \\ 4 & -1 \end{bmatrix}$

$\begin{bmatrix} 0 & -2 \\ 2 & 0 \end{bmatrix}$

$\begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}$

$\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$

Solution

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