Questions: [-6 -1 -4 -2] = [5 1 2 2] A

Solution Steps

To solve for matrix \( A \) in the equation \( \left[\begin{array}{ll}-6 & -1 \\ -4 & -2\end{array}\right]=\left[\begin{array}{ll}5 & 1 \\ 2 & 2\end{array}\right] A \), we need to find the inverse of the matrix on the right side and then multiply it by the matrix on the left side. This will give us the matrix \( A \).

We start with the equation:

\[ \left[\begin{array}{ll}-6 & -1 \\ -4 & -2\end{array}\right] = \left[\begin{array}{ll}5 & 1 \\ 2 & 2\end{array}\right] A \]

Let \( B = \left[\begin{array}{ll}-6 & -1 \\ -4 & -2\end{array}\right] \) and \( C = \left[\begin{array}{ll}5 & 1 \\ 2 & 2\end{array}\right] \).

To isolate \( A \), we need to find the inverse of matrix \( C \):

\[ C^{-1} = \left[\begin{array}{ll}0.25 & -0.125 \\ -0.25 & 0.625\end{array}\right] \]

Now, we can find \( A \) by multiplying the inverse of \( C \) with \( B \):

\[ A = C^{-1} B = \left[\begin{array}{ll}0.25 & -0.125 \\ -0.25 & 0.625\end{array}\right] \left[\begin{array}{ll}-6 & -1 \\ -4 & -2\end{array}\right] \]

Calculating this gives us:

\[ A = \left[\begin{array}{ll}-1 & 0 \\ -1 & -1\end{array}\right] \]

Final Answer