Perform the indicated operation, if possible. 7 9 -9 80-15 2 8 -4 11 -2 7 - 109 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The resulting matrix is O B. The matrices cannot be added.
Perform the indicated operation, if possible. 7 9 -9 80-15 2 8 -4 11 -2 7 - 109 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The resulting matrix is O B. The matrices cannot be added.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Matrix Addition Question
#### Problem Statement:
Perform the indicated operation, if possible.
\[
\begin{bmatrix}
3 & 7 & 9 & -9 \\
8 & -4 & 11 & 2
\end{bmatrix}
+
\begin{bmatrix}
8 & 0 & -15 & 2 \\
-2 & 7 & -10 & 9
\end{bmatrix}
\]
#### Instructions:
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
#### Choices:
- A. The resulting matrix is \[ \boxed{\phantom{A}} \].
- B. The matrices cannot be added.
#### Explanation:
To add two matrices, their dimensions must be identical. In this case, both matrices are 2x4 matrices (2 rows and 4 columns each). Thus, matrix addition is possible.
**Step-by-Step Solution:**
Add corresponding elements from each matrix:
1. First row, first element: \( 3 + 8 = 11 \)
2. First row, second element: \( 7 + 0 = 7 \)
3. First row, third element: \( 9 + (-15) = -6 \)
4. First row, fourth element: \( -9 + 2 = -7 \)
5. Second row, first element: \( 8 + (-2) = 6 \)
6. Second row, second element: \( -4 + 7 = 3 \)
7. Second row, third element: \( 11 + (-10) = 1 \)
8. Second row, fourth element: \( 2 + 9 = 11 \)
So, the resulting matrix is:
\[
\begin{bmatrix}
11 & 7 & -6 & -7 \\
6 & 3 & 1 & 11
\end{bmatrix}
\]
### Final Answer:
- A. The resulting matrix is \[ \begin{bmatrix} 11 & 7 & -6 & -7 \\ 6 & 3 & 1 & 11 \end{bmatrix} \].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F57708f6a-cbd4-4295-9f28-330268fec57a%2F5085551a-7241-46a7-a9ef-3512cf12a68e%2F4oozr6o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Matrix Addition Question
#### Problem Statement:
Perform the indicated operation, if possible.
\[
\begin{bmatrix}
3 & 7 & 9 & -9 \\
8 & -4 & 11 & 2
\end{bmatrix}
+
\begin{bmatrix}
8 & 0 & -15 & 2 \\
-2 & 7 & -10 & 9
\end{bmatrix}
\]
#### Instructions:
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
#### Choices:
- A. The resulting matrix is \[ \boxed{\phantom{A}} \].
- B. The matrices cannot be added.
#### Explanation:
To add two matrices, their dimensions must be identical. In this case, both matrices are 2x4 matrices (2 rows and 4 columns each). Thus, matrix addition is possible.
**Step-by-Step Solution:**
Add corresponding elements from each matrix:
1. First row, first element: \( 3 + 8 = 11 \)
2. First row, second element: \( 7 + 0 = 7 \)
3. First row, third element: \( 9 + (-15) = -6 \)
4. First row, fourth element: \( -9 + 2 = -7 \)
5. Second row, first element: \( 8 + (-2) = 6 \)
6. Second row, second element: \( -4 + 7 = 3 \)
7. Second row, third element: \( 11 + (-10) = 1 \)
8. Second row, fourth element: \( 2 + 9 = 11 \)
So, the resulting matrix is:
\[
\begin{bmatrix}
11 & 7 & -6 & -7 \\
6 & 3 & 1 & 11
\end{bmatrix}
\]
### Final Answer:
- A. The resulting matrix is \[ \begin{bmatrix} 11 & 7 & -6 & -7 \\ 6 & 3 & 1 & 11 \end{bmatrix} \].
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