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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Last row pls
![**Matrix Row Operation Example**
Consider the matrix:
\[
\begin{pmatrix}
1 & 0 & -1 \\
2 & 3 & 4 \\
-2 & 1 & -1 \\
\end{pmatrix}
\]
To perform the row operation \( R3 - 2R2 \), follow these steps:
1. Identify and modify the third row (\(R3\)) by subtracting two times the second row (\(2R2\)) from it.
2. The matrix becomes:
\[
\begin{pmatrix}
1 & 0 & -1 \\
2 & 3 & 4 \\
0 & 2 & 3 \\
\end{pmatrix}
\]
**Explanation:**
- The first row remains unchanged: \( (1, 0, -1) \).
- The operation \( R3 - 2R2 \) is applied to the third row:
- The first element: \(-2 - 2(2) = 0\).
- The second element: \(1 - 2(3) = 2\).
- The third element: \(-1 - 2(4) = 3\).
- The second row \( (2, 3, 4) \) remains unchanged.
This procedure illustrates how basic row operations can transform matrices in linear algebra.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ebe91de-3090-46ac-907f-d0393c4d1db8%2F95a1b9c1-fd41-4a9d-b3e2-5e6900d57704%2F7knmzha_processed.png&w=3840&q=75)
Transcribed Image Text:**Matrix Row Operation Example**
Consider the matrix:
\[
\begin{pmatrix}
1 & 0 & -1 \\
2 & 3 & 4 \\
-2 & 1 & -1 \\
\end{pmatrix}
\]
To perform the row operation \( R3 - 2R2 \), follow these steps:
1. Identify and modify the third row (\(R3\)) by subtracting two times the second row (\(2R2\)) from it.
2. The matrix becomes:
\[
\begin{pmatrix}
1 & 0 & -1 \\
2 & 3 & 4 \\
0 & 2 & 3 \\
\end{pmatrix}
\]
**Explanation:**
- The first row remains unchanged: \( (1, 0, -1) \).
- The operation \( R3 - 2R2 \) is applied to the third row:
- The first element: \(-2 - 2(2) = 0\).
- The second element: \(1 - 2(3) = 2\).
- The third element: \(-1 - 2(4) = 3\).
- The second row \( (2, 3, 4) \) remains unchanged.
This procedure illustrates how basic row operations can transform matrices in linear algebra.
Expert Solution
Step 1
Given query is to perform the indicated matrix operation.
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