Let's solve the problem step-by-step.
We need to perform the following operations on the given matrices:
1. Add the corresponding elements of the two matrices.
2. Subtract 30 from each resulting element.
The given matrices are:
[tex]\[
\mathbf{A} = \begin{pmatrix}
-8 & -3 & 1 \\
5 & -2 & -8 \\
4 & 0 & 12
\end{pmatrix}
\][/tex]
[tex]\[
\mathbf{B} = \begin{pmatrix}
-5 & 1 & -11 \\
-4 & 0 & -15 \\
3 & 10 & 21
\end{pmatrix}
\][/tex]
### Step 1: Add corresponding elements of matrices A and B
Let's compute the addition of matrices [tex]\(\mathbf{A}\)[/tex] and [tex]\(\mathbf{B}\)[/tex]:
[tex]\[
\mathbf{A} + \mathbf{B} =
\begin{pmatrix}
-8 + (-5) & -3 + 1 & 1 + (-11) \\
5 + (-4) & -2 + 0 & -8 + (-15) \\
4 + 3 & 0 + 10 & 12 + 21
\end{pmatrix}
\][/tex]
Calculating each element:
[tex]\[
\mathbf{A} + \mathbf{B} =
\begin{pmatrix}
-8 - 5 & -3 + 1 & 1 - 11 \\
5 - 4 & -2 + 0 & -8 - 15 \\
4 + 3 & 0 + 10 & 12 + 21
\end{pmatrix}
=
\begin{pmatrix}
-13 & -2 & -10 \\
1 & -2 & -23 \\
7 & 10 & 33
\end{pmatrix}
\][/tex]
### Step 2: Subtract 30 from each element
Next, we subtract 30 from every element of the resultant matrix:
[tex]\[
\mathbf{Result} =
\begin{pmatrix}
-13 - 30 & -2 - 30 & -10 - 30 \\
1 - 30 & -2 - 30 & -23 - 30 \\
7 - 30 & 10 - 30 & 33 - 30
\end{pmatrix}
=
\begin{pmatrix}
-43 & -32 & -40 \\
-29 & -32 & -53 \\
-23 & -20 & 3
\end{pmatrix}
\][/tex]
So, the final result is:
[tex]\[
\begin{pmatrix}
-43 & -32 & -40 \\
-29 & -32 & -53 \\
-23 & -20 & 3
\end{pmatrix}
\][/tex]
