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



Answer :

To find the sum of two matrices [tex]\( A \)[/tex] and [tex]\( B \)[/tex], you add their corresponding elements. Here's a detailed step-by-step solution:

Given matrices:
[tex]\[ A = \begin{bmatrix} 3 & -1 \\ 2 & 0 \\ -3 & 3 \end{bmatrix} \][/tex]
[tex]\[ B = \begin{bmatrix} 3 & 3 \\ -5 & 4 \\ -4 & 2 \end{bmatrix} \][/tex]

We will calculate the sum [tex]\( A + B \)[/tex] by adding each corresponding element of matrices [tex]\( A \)[/tex] and [tex]\( B \)[/tex]:

1. First row, first column:
[tex]\[ 3 + 3 = 6 \][/tex]
2. First row, second column:
[tex]\[ -1 + 3 = 2 \][/tex]
3. Second row, first column:
[tex]\[ 2 - 5 = -3 \][/tex]
4. Second row, second column:
[tex]\[ 0 + 4 = 4 \][/tex]
5. Third row, first column:
[tex]\[ -3 - 4 = -7 \][/tex]
6. Third row, second column:
[tex]\[ 3 + 2 = 5 \][/tex]

Putting these results together, the resulting matrix [tex]\( A + B \)[/tex] is:
[tex]\[ A + B = \begin{bmatrix} 6 & 2 \\ -3 & 4 \\ -7 & 5 \end{bmatrix} \][/tex]

Thus, the sum of the given matrices [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is:
[tex]\[ \begin{bmatrix} 6 & 2 \\ -3 & 4 \\ -7 & 5 \end{bmatrix} \][/tex]