Determine whether b is in col(A) and whether w is in row(A). 1 1 -1 1 400-0--- b = 3 W = 5 -1 -7 2 A = 1 5 b is in col(A) Yes No w is in row(A) Yes No [1 1 -7 -3
Determine whether b is in col(A) and whether w is in row(A). 1 1 -1 1 400-0--- b = 3 W = 5 -1 -7 2 A = 1 5 b is in col(A) Yes No w is in row(A) Yes No [1 1 -7 -3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Title: Analyzing Vector Inclusion in Matrix Columns and Rows**
**Objective: Determine whether vector b is in the column space of matrix A (col(A)) and whether vector w is in the row space of A (row(A)).**
---
**Matrix and Vectors Defined:**
- Matrix \( A \):
\[
A = \begin{bmatrix}
1 & 1 & -1 \\
1 & 5 & 0 \\
5 & -1 & -7
\end{bmatrix}
\]
- Vector \( b \):
\[
b = \begin{bmatrix}
1 \\
3 \\
2
\end{bmatrix}
\]
- Vector \( w \):
\[
w = \begin{bmatrix}
1 & -7 & -3
\end{bmatrix}
\]
---
**Questions:**
1. **b is in col(A)**
- ☐ Yes
- ☐ No
2. **w is in row(A)**
- ☐ Yes
- ☐ No
---
**Instructions:**
To determine if vector \( b \) is in the column space of \( A \), check if there exists a solution to the matrix equation \( A\mathbf{x} = \mathbf{b} \).
To determine if vector \( w \) is in the row space of \( A \), check if \( w \) can be expressed as a linear combination of the rows of \( A \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6948d5d-782c-4f32-af22-abf47b4c3397%2F6eb84810-01f4-4c47-88cf-d08b3bea2621%2Fff0her_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Analyzing Vector Inclusion in Matrix Columns and Rows**
**Objective: Determine whether vector b is in the column space of matrix A (col(A)) and whether vector w is in the row space of A (row(A)).**
---
**Matrix and Vectors Defined:**
- Matrix \( A \):
\[
A = \begin{bmatrix}
1 & 1 & -1 \\
1 & 5 & 0 \\
5 & -1 & -7
\end{bmatrix}
\]
- Vector \( b \):
\[
b = \begin{bmatrix}
1 \\
3 \\
2
\end{bmatrix}
\]
- Vector \( w \):
\[
w = \begin{bmatrix}
1 & -7 & -3
\end{bmatrix}
\]
---
**Questions:**
1. **b is in col(A)**
- ☐ Yes
- ☐ No
2. **w is in row(A)**
- ☐ Yes
- ☐ No
---
**Instructions:**
To determine if vector \( b \) is in the column space of \( A \), check if there exists a solution to the matrix equation \( A\mathbf{x} = \mathbf{b} \).
To determine if vector \( w \) is in the row space of \( A \), check if \( w \) can be expressed as a linear combination of the rows of \( A \).
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