Answer :
Let's solve the given problem step by step. We need to compute the expression:
[tex]$ \left[\begin{array}{cc}3 & 0 \\ 8 & -4 \\ 0 & -5\end{array}\right] - 4 \left[\begin{array}{cc}0 & -3 \\ 2 & 1 \\ -1 & 2\end{array}\right] $[/tex]
1. Scale the second matrix by 4:
[tex]\[ 4 \left[\begin{array}{cc}0 & -3 \\ 2 & 1 \\ -1 & 2\end{array}\right] = \left[\begin{array}{cc}0 \cdot 4 & -3 \cdot 4 \\ 2 \cdot 4 & 1 \cdot 4 \\ -1 \cdot 4 & 2 \cdot 4\end{array}\right] = \left[\begin{array}{cc}0 & -12 \\ 8 & 4 \\ -4 & 8\end{array}\right] \][/tex]
2. Subtract the scaled matrix from the first matrix:
[tex]\[ \left[\begin{array}{cc}3 & 0 \\ 8 & -4 \\ 0 & -5\end{array}\right] - \left[\begin{array}{cc}0 & -12 \\ 8 & 4 \\ -4 & 8\end{array}\right] = \left[\begin{array}{cc}3-0 & 0-(-12) \\ 8-8 & -4-4 \\ 0-(-4) & -5-8\end{array}\right] \][/tex]
Performing the element-wise operations:
[tex]\[ = \left[\begin{array}{cc}3 & 0+12 \\ 8-8 & -4-4 \\ 0+4 & -5-8\end{array}\right] = \left[\begin{array}{cc}3 & 12 \\ 0 & -8 \\ 4 & -13\end{array}\right] \][/tex]
So, the result of the matrix subtraction is:
[tex]\[ \left[\begin{array}{cc}3 & 12 \\ 0 & -8 \\ 4 & -13\end{array}\right] \][/tex]
[tex]$ \left[\begin{array}{cc}3 & 0 \\ 8 & -4 \\ 0 & -5\end{array}\right] - 4 \left[\begin{array}{cc}0 & -3 \\ 2 & 1 \\ -1 & 2\end{array}\right] $[/tex]
1. Scale the second matrix by 4:
[tex]\[ 4 \left[\begin{array}{cc}0 & -3 \\ 2 & 1 \\ -1 & 2\end{array}\right] = \left[\begin{array}{cc}0 \cdot 4 & -3 \cdot 4 \\ 2 \cdot 4 & 1 \cdot 4 \\ -1 \cdot 4 & 2 \cdot 4\end{array}\right] = \left[\begin{array}{cc}0 & -12 \\ 8 & 4 \\ -4 & 8\end{array}\right] \][/tex]
2. Subtract the scaled matrix from the first matrix:
[tex]\[ \left[\begin{array}{cc}3 & 0 \\ 8 & -4 \\ 0 & -5\end{array}\right] - \left[\begin{array}{cc}0 & -12 \\ 8 & 4 \\ -4 & 8\end{array}\right] = \left[\begin{array}{cc}3-0 & 0-(-12) \\ 8-8 & -4-4 \\ 0-(-4) & -5-8\end{array}\right] \][/tex]
Performing the element-wise operations:
[tex]\[ = \left[\begin{array}{cc}3 & 0+12 \\ 8-8 & -4-4 \\ 0+4 & -5-8\end{array}\right] = \left[\begin{array}{cc}3 & 12 \\ 0 & -8 \\ 4 & -13\end{array}\right] \][/tex]
So, the result of the matrix subtraction is:
[tex]\[ \left[\begin{array}{cc}3 & 12 \\ 0 & -8 \\ 4 & -13\end{array}\right] \][/tex]
