Question

Find the sum of two matrices.
0 8 -8 3
2 4 7 6
-3 7 13 -11
0 -6 4 8

Answer 1

To find the sum of two matrices, you simply add the corresponding elements from each matrix.

Let's denote the first matrix as \( A \) and the second matrix as \( B \):

Matrix \( A \):
\[
\begin{bmatrix}
0 & 8 \\
2 & 4 \\
-3 & 7 \\
0 & -6
\end{bmatrix}
\]

Matrix \( B \):
\[
\begin{bmatrix}
-8 & 3 \\
7 & 6 \\
13 & -11 \\
4 & 8
\end{bmatrix}
\]

Now we will add \( A \) and \( B \):

\[
A + B =
\begin{bmatrix}
0 + (-8) & 8 + 3 \\
2 + 7 & 4 + 6 \\
-3 + 13 & 7 + (-11) \\
0 + 4 & -6 + 8
\end{bmatrix}
\]

Calculating each element:

1. \( 0 + (-8) = -8 \)
2. \( 8 + 3 = 11 \)
3. \( 2 + 7 = 9 \)
4. \( 4 + 6 = 10 \)
5. \( -3 + 13 = 10 \)
6. \( 7 + (-11) = -4 \)
7. \( 0 + 4 = 4 \)
8. \( -6 + 8 = 2 \)

Putting this together, the resultant matrix \( C = A + B \) is:

\[
C =
\begin{bmatrix}
-8 & 11 \\
9 & 10 \\
10 & -4 \\
4 & 2
\end{bmatrix}
\]

Thus, the sum of the two matrices is:

\[
\begin{bmatrix}
-8 & 11 \\
9 & 10 \\
10 & -4 \\
4 & 2
\end{bmatrix}
\]