Answer
$\begin{bmatrix} 6&-2\\ 2&12 \end{bmatrix}$
Work Step by Step
Step 1. List the matrices needed:
$\begin{array} \\A=\\ \end{array}
\begin{bmatrix} 2&1\\ 3&2 \end{bmatrix},
\begin{array} \\B=\\ \end{array}
\begin{bmatrix} 1&-2\\ -2&4 \end{bmatrix} $
Step 2. Solve X from the equation: $X=2A+2B=2(A+B)$
Step 3. Perform the operation:
$\begin{array} \\A+B=\\ \end{array}
\begin{bmatrix} 2&1\\ 3&2 \end{bmatrix}+
\begin{bmatrix} 1&-2\\ -2&4 \end{bmatrix}
=\begin{bmatrix} 3&-1\\ 1&6 \end{bmatrix}$
Step 4. Write the solution:
$\begin{array} \\X=2(A+B)=2\\ \end{array}
\begin{bmatrix} 3&-1\\ 1&6 \end{bmatrix}
=\begin{bmatrix} 6&-2\\ 2&12 \end{bmatrix}$
