The sum of two matrices is found by adding the corresponding elements from each matrix.
Given the matrices:
[tex]\[
\text{Matrix 1} = \begin{pmatrix} 3 & 9 \\ 5 & -2 \end{pmatrix}
\][/tex]
[tex]\[
\text{Matrix 2} = \begin{pmatrix} 6 & 0 \\ -8 & 4 \end{pmatrix}
\][/tex]
We perform the addition element-wise, which means adding the elements in the same positions from each matrix.
1. Top-Left Element:
[tex]\[
3 (from\ Matrix\ 1) + 6 (from\ Matrix\ 2) = 3 + 6 = 9
\][/tex]
2. Top-Right Element:
[tex]\[
9 (from\ Matrix\ 1) + 0 (from\ Matrix\ 2) = 9 + 0 = 9
\][/tex]
3. Bottom-Left Element:
[tex]\[
5 (from\ Matrix\ 1) + -8 (from\ Matrix\ 2) = 5 + (-8) = 5 - 8 = -3
\][/tex]
4. Bottom-Right Element:
[tex]\[
-2 (from\ Matrix\ 1) + 4 (from\ Matrix\ 2) = -2 + 4 = 2
\][/tex]
Combining these results, the resultant matrix, or the sum of the given matrices, is:
[tex]\[
\begin{pmatrix}
9 & 9 \\
-3 & 2
\end{pmatrix}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\begin{pmatrix}
9 & 9 \\
-3 & 2
\end{pmatrix}
\][/tex]
