MathAlgebraLinear algebraLinear operators

Linear operators and matrices

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Consider a linear operator in $\mathbb{R}^2$ with the matrix

$A=\begin{pmatrix} a_{11} & a_{12}\\ a_{21} & a_{22} \end{pmatrix}$ How would look the matrix of the operator that first applies operator $A$ and then multiplies every coordinate of the result by 2?

Select one option from the list

\begin{pmatrix} \sqrt{2} a_{11} & \sqrt{2} a_{12}\\ \sqrt{2} a_{21} & \sqrt{2} a_{22} \end{pmatrix}

\begin{pmatrix} 2a_{11} & a_{12}\\ a_{21} & 2a_{22} \end{pmatrix}

\begin{pmatrix} a_{11} + 2 & a_{12} + 2\\ a_{21} + 2 & a_{22} + 2 \end{pmatrix}

\begin{pmatrix} 2 a_{11} & 2 a_{12}\\ 2a_{21} & 2a_{22} \end{pmatrix}

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