To find the sum [tex]\(A + B\)[/tex] of matrices [tex]\(A\)[/tex] and [tex]\(B\)[/tex], we need to add their corresponding elements.
Given matrices:
[tex]\[
A = \begin{pmatrix}
2 & -1 \\
5 & -2 \\
-3 & 4
\end{pmatrix}
\][/tex]
[tex]\[
B = \begin{pmatrix}
6 & -1 \\
-6 & 5 \\
-1 & 0
\end{pmatrix}
\][/tex]
The sum of these matrices is calculated as follows:
For the element in the first row, first column:
[tex]\[
2 + 6 = 8
\][/tex]
For the element in the first row, second column:
[tex]\[
-1 + (-1) = -2
\][/tex]
For the element in the second row, first column:
[tex]\[
5 + (-6) = -1
\][/tex]
For the element in the second row, second column:
[tex]\[
-2 + 5 = 3
\][/tex]
For the element in the third row, first column:
[tex]\[
-3 + (-1) = -4
\][/tex]
For the element in the third row, second column:
[tex]\[
4 + 0 = 4
\][/tex]
Thus, the resulting matrix [tex]\(A + B\)[/tex] is:
[tex]\[
A + B = \begin{pmatrix}
8 & -2 \\
-1 & 3 \\
-4 & 4
\end{pmatrix}
\][/tex]
Therefore, the correct option is:
[tex]\[
\begin{pmatrix}
8 & -2 \\
-1 & 3 \\
-4 & 4
\end{pmatrix}
\][/tex]
From the given options, this corresponds to:
[tex]\[
\boxed{\begin{array}{cc}
8 & -2 \\
-1 & 3 \\
-4 & 4 \\
\end{array}}
\][/tex]
