To perform the matrix addition [tex]\( A + B \)[/tex], we need to add the corresponding elements of matrices [tex]\( A \)[/tex] and [tex]\( B \)[/tex].
Given matrices:
[tex]\[ A = \begin{bmatrix}
0 & 5 & -2 \\
1 & 3 & 2
\end{bmatrix} \][/tex]
[tex]\[ B = \begin{bmatrix}
7 & 1 & 0 \\
-1 & 5 & -7
\end{bmatrix} \][/tex]
We add the elements at each corresponding position:
1. For the element in the first row, first column:
[tex]\[ 0 + 7 = 7 \][/tex]
2. For the element in the first row, second column:
[tex]\[ 5 + 1 = 6 \][/tex]
3. For the element in the first row, third column:
[tex]\[ -2 + 0 = -2 \][/tex]
4. For the element in the second row, first column:
[tex]\[ 1 + (-1) = 0 \][/tex]
5. For the element in the second row, second column:
[tex]\[ 3 + 5 = 8 \][/tex]
6. For the element in the second row, third column:
[tex]\[ 2 + (-7) = -5 \][/tex]
Thus, the resulting matrix [tex]\( A + B \)[/tex] is:
[tex]\[ A + B = \begin{bmatrix}
7 & 6 & -2 \\
0 & 8 & -5
\end{bmatrix} \][/tex]
So, the completed matrix is:
[tex]\[ A + B = \begin{bmatrix}
7 & 6 & -2 \\
0 & 8 & -5
\end{bmatrix} \][/tex]
Select the correct choice below:
[tex]\[ \boxed{A + B = \begin{bmatrix}
7 & 6 & -2 \\
0 & 8 & -5
\end{bmatrix}} \][/tex]
This is the correct result of the matrix addition [tex]\( A + B \)[/tex].
