Answer
$\begin{bmatrix} \frac{7}{2}&-2\\ 0&8 \end{bmatrix}$
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: $X=A+\frac{3}{2}B$
Step 3. Perform the operation:
$\begin{array} \\A+\frac{3}{2}B=\\ \end{array}
\begin{bmatrix} 2&1\\ 3&2 \end{bmatrix}+
\begin{bmatrix} \frac{3}{2}&-3\\ -3&6 \end{bmatrix}
=\begin{bmatrix} \frac{7}{2}&-2\\ 0&8 \end{bmatrix}$
Step 4. Write the solution:
$\begin{array} \\X=\\ \end{array}
\begin{bmatrix} \frac{7}{2}&-2\\ 0&8 \end{bmatrix}$
