Question

Matrices A and B are shown below.
A= -2 3 B= 5 -4
0 -1 -2 -4

Answer 1

Which matrix represents the sum of A and B

Answer 2

It looks like you have provided two matrices \( A \) and \( B \) as follows:

\[
A = \begin{pmatrix}
-2 & 3 \\
0 & -1
\end{pmatrix}
\]

\[
B = \begin{pmatrix}
5 & -4 \\
-2 & -4
\end{pmatrix}
\]

Would you like to perform specific operations with these matrices, such as addition, subtraction, multiplication, finding the determinant, or something else? Please let me know!

Answer 3

To find the sum of matrices \( A \) and \( B \), you simply add the corresponding elements of each matrix.

Given:

\[
A = \begin{pmatrix}
-2 & 3 \\
0 & -1
\end{pmatrix}
\]

\[
B = \begin{pmatrix}
5 & -4 \\
-2 & -4
\end{pmatrix}
\]

The sum \( C = A + B \) is computed as follows:

\[
C = \begin{pmatrix}
-2 + 5 & 3 + (-4) \\
0 + (-2) & -1 + (-4)
\end{pmatrix}
\]

Calculating each element:

- First row, first column: \(-2 + 5 = 3\)
- First row, second column: \(3 - 4 = -1\)
- Second row, first column: \(0 - 2 = -2\)
- Second row, second column: \(-1 - 4 = -5\)

Putting it all together, we get:

\[
C = \begin{pmatrix}
3 & -1 \\
-2 & -5
\end{pmatrix}
\]

So, the sum of matrices \( A \) and \( B \) is:

\[
\begin{pmatrix}
3 & -1 \\
-2 & -5
\end{pmatrix}
\]