Given the matrices \( A \) and \( B \) shown below, find \( -A-4 B \).
\[
A=\left[\begin{array}{cc}
-2 & 0 \\
3 & -5 \\
0 & 4 \\
2 & 5
\end{array}\right] \quad B=\left[\begin{array}{cc}
-6 & 4 \\
-2 & 4 \\
1 & 5 \\
3 & 2
\end{array}\right]
\]
Rows: \( 2 \odot \odot \) Columns: \( 2 \odot \oplus \)
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Answer
(-A-4B) = \left[\begin{array}{cc} 2+24 & 0-16 \\ -3+8 & 5-16 \\ 0-4 & -4-20 \\ -2-12 & -5-8 \end{array}\right] = \left[\begin{array}{cc} 26 & -16 \\ 5 & -11 \\ -4 & -24 \\ -14 & -13 \end{array}\right]
Step 1 ：(-1)A = \left[\begin{array}{cc} 2 & 0 \\ -3 & 5 \\ 0 & -4 \\ -2 & -5 \end{array}\right]
Step 2 ：(-4)B = \left[\begin{array}{cc} 24 & -16 \\ 8 & -16 \\ -4 & -20 \\ -12 & -8 \end{array}\right]
Step 3 ：(-A-4B) = \left[\begin{array}{cc} 2+24 & 0-16 \\ -3+8 & 5-16 \\ 0-4 & -4-20 \\ -2-12 & -5-8 \end{array}\right] = \left[\begin{array}{cc} 26 & -16 \\ 5 & -11 \\ -4 & -24 \\ -14 & -13 \end{array}\right]
