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]
