Question

Find the sum. ⎡⎣⎢−140−2020−1542⎤⎦⎥+⎡⎣⎢−5202510−456⎤⎦⎥ Complete the matrix that represents the sum. (1 point) ⎡⎣⎢−140−2020−1542⎤⎦⎥+⎡⎣⎢−5202510−456⎤⎦⎥= $$

Answer 1

To find the sum of the two matrices, we add the corresponding elements together.

Given matrices:
\[
\begin{bmatrix}
-140 & -20 & 20 \\
-15 & 4 & 2
\end{bmatrix}
\]
and
\[
\begin{bmatrix}
-5 & 2025 & 10 \\
-45 & 6 & 0
\end{bmatrix}
\]

We will add them element-wise.

1. **First row, first column**:
\(-140 + (-5) = -145\)

2. **First row, second column**:
\(-20 + 2025 = 2005\)

3. **First row, third column**:
\(20 + 10 = 30\)

4. **Second row, first column**:
\(-15 + (-45) = -60\)

5. **Second row, second column**:
\(4 + 6 = 10\)

6. **Second row, third column**:
\(2 + 0 = 2\)

Now we compile the results into a new matrix:

\[
\begin{bmatrix}
-145 & 2005 & 30 \\
-60 & 10 & 2
\end{bmatrix}
\]

Thus, the result of the matrix sum is:

\[
\begin{bmatrix}
-145 & 2005 & 30 \\
-60 & 10 & 2
\end{bmatrix}
\]