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Use the following matrices to perform the addition [tex]A + B[/tex].

[tex]\[
A=\begin{bmatrix}
0 & 5 & -2 \\
1 & 3 & 2
\end{bmatrix} \text{ and } B=\begin{bmatrix}
7 & 1 & 0 \\
-1 & 5 & -7
\end{bmatrix}
\][/tex]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A.
[tex]\[
A+B=\begin{bmatrix}
\square & \square & \square \\
\square & \square & \square
\end{bmatrix}
\][/tex]


Sagot :

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].