$A = \begin{bmatrix}2 & 5 \\ -1 & 3\end{bmatrix}$ is written as $P + Q$ , with $P$ symmetric and $Q$ skew-symmetric. What is $Q$ ?

\begin{bmatrix}0 & -3 \\ 3 & 0\end{bmatrix}

Correct answerYour answer

\begin{bmatrix}0 & 6 \\ -6 & 0\end{bmatrix}

Correct answerYour answer

\begin{bmatrix}2 & 2 \\ 2 & 3\end{bmatrix}

Correct answerYour answer

\begin{bmatrix}0 & 3 \\ -3 & 0\end{bmatrix}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$Q = \frac{1}{2}(A - A')$ .
$A - A' = \begin{bmatrix}0 & 6 \\ -6 & 0\end{bmatrix}$ , so $Q = \begin{bmatrix}0 & 3 \\ -3 & 0\end{bmatrix}$ .

Worth noting

$\begin{bmatrix}0 & -3 \\ 3 & 0\end{bmatrix}$ is $\frac{1}{2}(A' - A)$ : the subtraction was done the wrong way round.

Ten questions from Matrices, at your own pace.

A=[25−13]A = \begin{bmatrix}2 & 5 \\ -1 & 3\end{bmatrix}A=[2−1​53​] is written as P+QP + QP+Q, with PPP symmetric and QQQ skew-symmetric. What is QQQ?