To find the sum of two matrices, you simply add the corresponding elements of each matrix together. Let's break this down step-by-step for the given matrices:
The first matrix is:
[tex]\[
\begin{pmatrix}
4 & 19 & -5 \\
7 & 0 & -14
\end{pmatrix}
\][/tex]
The second matrix is:
[tex]\[
\begin{pmatrix}
-8 & 7 & 0 \\
-1 & 17 & 6
\end{pmatrix}
\][/tex]
Now, let's add the corresponding elements from both matrices.
1. For the element in the first row, first column:
[tex]\[
4 + (-8) = -4
\][/tex]
2. For the element in the first row, second column:
[tex]\[
19 + 7 = 26
\][/tex]
3. For the element in the first row, third column:
[tex]\[
-5 + 0 = -5
\][/tex]
4. For the element in the second row, first column:
[tex]\[
7 + (-1) = 6
\][/tex]
5. For the element in the second row, second column:
[tex]\[
0 + 17 = 17
\][/tex]
6. For the element in the second row, third column:
[tex]\[
-14 + 6 = -8
\][/tex]
Combining all these results, the sum of the two matrices is:
[tex]\[
\begin{pmatrix}
-4 & 26 & -5 \\
6 & 17 & -8
\end{pmatrix}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\left[\begin{array}{ccc}-4 & 26 & -5 \\ 6 & 17 & -8\end{array}\right]
\][/tex]
