If matrix A, what is A + A'?

Question 77

EasyOriginal question

If $A = \begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}$ , what is $A + A'$ ?

\begin{bmatrix}2 & 4 \\ 6 & 8\end{bmatrix}

Correct answerYour answer

\begin{bmatrix}2 & 6 \\ 4 & 8\end{bmatrix}

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

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\begin{bmatrix}2 & 5 \\ 5 & 8\end{bmatrix}

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Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$A' = \begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix}$ , the rows of $A$ written as columns.
$A + A' = \begin{bmatrix}2 & 5 \\ 5 & 8\end{bmatrix}$ , a symmetric matrix.

Worth noting

$2A$ adds $A$ to itself, not to its transpose.

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