Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![### Row Transformation of a Matrix
#### Task
Use the specified row transformation to change the given matrix using the operation \(7R_1 + R_2\).
#### Given Matrix
\[
\begin{bmatrix}
1 & 4 & 5 \\
-7 & 2 & -1 \\
9 & 7 & 0
\end{bmatrix}
\]
#### Row Transformation
- Apply the transformation \(7R_1 + R_2\) to the matrix.
#### Matrix Operation
1. **Identify Rows**:
- \(R_1\) = [1, 4, 5]
- \(R_2\) = [-7, 2, -1]
- \(R_3\) = [9, 7, 0]
2. **Perform the Operation**:
- Replace \(R_2\) with the result of \(7R_1 + R_2\).
- Calculate \(7R_1\):
\[
7 \times R_1 = [7 \times 1, 7 \times 4, 7 \times 5] = [7, 28, 35]
\]
- Add this to \(R_2\):
\[
[7, 28, 35] + [-7, 2, -1] = [0, 30, 34]
\]
3. **Resulting Matrix**:
\[
\begin{bmatrix}
1 & 4 & 5 \\
0 & 30 & 34 \\
9 & 7 & 0
\end{bmatrix}
\]
### Conclusion
The matrix after applying the transformation \(7R_1 + R_2\) to \(R_2\) is:
\[
\begin{bmatrix}
1 & 4 & 5 \\
0 & 30 & 34 \\
9 & 7 & 0
\end{bmatrix}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29ad9625-8bb4-4466-8385-f817dba6df9d%2Fbff2fe92-3587-47ab-b01a-917758d0d1c4%2Flqn7kvn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Row Transformation of a Matrix
#### Task
Use the specified row transformation to change the given matrix using the operation \(7R_1 + R_2\).
#### Given Matrix
\[
\begin{bmatrix}
1 & 4 & 5 \\
-7 & 2 & -1 \\
9 & 7 & 0
\end{bmatrix}
\]
#### Row Transformation
- Apply the transformation \(7R_1 + R_2\) to the matrix.
#### Matrix Operation
1. **Identify Rows**:
- \(R_1\) = [1, 4, 5]
- \(R_2\) = [-7, 2, -1]
- \(R_3\) = [9, 7, 0]
2. **Perform the Operation**:
- Replace \(R_2\) with the result of \(7R_1 + R_2\).
- Calculate \(7R_1\):
\[
7 \times R_1 = [7 \times 1, 7 \times 4, 7 \times 5] = [7, 28, 35]
\]
- Add this to \(R_2\):
\[
[7, 28, 35] + [-7, 2, -1] = [0, 30, 34]
\]
3. **Resulting Matrix**:
\[
\begin{bmatrix}
1 & 4 & 5 \\
0 & 30 & 34 \\
9 & 7 & 0
\end{bmatrix}
\]
### Conclusion
The matrix after applying the transformation \(7R_1 + R_2\) to \(R_2\) is:
\[
\begin{bmatrix}
1 & 4 & 5 \\
0 & 30 & 34 \\
9 & 7 & 0
\end{bmatrix}
\]
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