Question 14, 6.4.23
Let $A=\left[\begin{array}{ll}-3 & -1 \\ -6 & -5\end{array}\right]$ and $B=\left[\begin{array}{ll}-6 & -1 \\ -5 & -2\end{array}\right]$. Find a matrix $X$ satisfying the given equation.
\[
2 X=-2 A+3 B
\]
$X=\square$ (Simplify your answer.)

Step 1 ：Given the matrices A and B as $A=\left[\begin{array}{ll}-3 & -1 \ -6 & -5\end{array}\right]$ and $B=\left[\begin{array}{ll}-6 & -1 \ -5 & -2\end{array}\right]$, we are asked to find a matrix X that satisfies the equation $2 X=-2 A+3 B$.

Step 2 ：First, we calculate -2A + 3B. This gives us the matrix $[-2A + 3B]=\left[\begin{array}{ll}-12 & -1 \ -3 & 4\end{array}\right]$.

Step 3 ：Next, we divide this result by 2 to find X. This gives us the matrix $X=\left[\begin{array}{ll}-6 & -0.5 \ -1.5 & 2\end{array}\right]$.

Step 4 ：Final Answer: The matrix $X$ that satisfies the given equation is $X=\boxed{\left[\begin{array}{ll}-6 & -0.5 \ -1.5 & 2\end{array}\right]}$.