Answer
$\begin{bmatrix} -\frac{1}{3}&-1\\ -\frac{5}{3}&\frac{2}{3} \end{bmatrix}$
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: $X=\frac{1}{3}(B-A)$
Step 3. Perform the operation:
$\begin{array} \\B-A=\\ \end{array}
\begin{bmatrix} 1&-2\\ -2&4 \end{bmatrix}-
\begin{bmatrix} 2&1\\ 3&2 \end{bmatrix}
=\begin{bmatrix} -1&-3\\ -5&2 \end{bmatrix}, $
Step 4. Write the solution:
$\begin{array} \\X=\frac{1}{3}(B-A)=\\ \end{array}
\frac{1}{3}\begin{bmatrix} -1&-3\\ -5&2 \end{bmatrix}
=\begin{bmatrix} -\frac{1}{3}&-1\\ -\frac{5}{3}&\frac{2}{3} \end{bmatrix}$
