Given matrix A = (
3 1 3
2 3 6
3 1 7
) and B = (
4 2 5
3 1 7
2 6 3
).

a) Find the value of matrix A + B

To find the sum of two matrices, \( A + B \), we add corresponding elements from each matrix.

Given matrices:

\[
A = \begin{pmatrix}
3 & 1 & 3 \\
2 & 3 & 6 \\
3 & 1 & 7
\end{pmatrix}
\]

\[
B = \begin{pmatrix}
4 & 2 & 5 \\
3 & 1 & 7 \\
2 & 6 & 3
\end{pmatrix}
\]

Let's compute \( A + B \):

\[
A + B = \begin{pmatrix}
3+4 & 1+2 & 3+5 \\
2+3 & 3+1 & 6+7 \\
3+2 & 1+6 & 7+3
\end{pmatrix}
\]

Simplifying the above:

\[
A + B = \begin{pmatrix}
7 & 3 & 8 \\
5 & 4 & 13 \\
5 & 7 & 10
\end{pmatrix}
\]

So, the value of \( A + B \) is:

\[
\begin{pmatrix}
7 & 3 & 8 \\
5 & 4 & 13 \\
5 & 7 & 10
\end{pmatrix}
\]

Would you like any more details or have any questions?

Here are 5 related questions for further exploration:

1. How do you subtract matrix \( B \) from matrix \( A \)?
2. What is the determinant of matrix \( A \)?
3. What is the transpose of matrix \( B \)?
4. Can you find the product of matrices \( A \) and \( B \)?
5. How do you determine if matrix \( A \) is invertible?

**Tip:** When adding or subtracting matrices, ensure they have the same dimensions to perform element-wise operations correctly.

Learn how to compute the sum of matrices A and B, step-by-step. Matrix addition involves adding corresponding elements from each matrix. Example matrices given are A = [3 1 3; 2 3 6; 3 1 7] and B = [4 2 5; 3 1 7; 2 6 3]. Get detailed insights into matrix operations suitable for high school students.

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