Answer :
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]
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]