Given [tex]\( A = \left[\begin{array}{cc}2 & -1 \\ 5 & -2 \\ -3 & 4\end{array}\right] \)[/tex] and [tex]\( B = \left[\begin{array}{cc}6 & -1 \\ -6 & 5 \\ -1 & 0\end{array}\right] \)[/tex], what is [tex]\( A+B \)[/tex]?

A. [tex]\(\left[\begin{array}{cc}-4 & -2 \\ -1 & -7 \\ -4 & 4\end{array}\right]\)[/tex]

B. [tex]\(\left[\begin{array}{cc}-4 & 0 \\ 11 & -7 \\ -2 & 4\end{array}\right]\)[/tex]

C. [tex]\(\left[\begin{array}{cc}8 & -2 \\ -1 & 3 \\ -4 & 4\end{array}\right]\)[/tex]

D. [tex]\(\left[\begin{array}{cc}8 & 0 \\ -1 & 3 \\ -4 & 0\end{array}\right]\)[/tex]



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]