Let u = 0 6 -1 and A = 48 4 103 12 1 Is u in the subset of R³ spanned by the columns of A? Why or why not? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal for each matrix element.) A. Yes, multiplying A by the vector writes u as a linear combination of the columns of A. B. No, the reduced echelon form of the augmented matrix is, which is an inconsistent system.
Let u = 0 6 -1 and A = 48 4 103 12 1 Is u in the subset of R³ spanned by the columns of A? Why or why not? Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal for each matrix element.) A. Yes, multiplying A by the vector writes u as a linear combination of the columns of A. B. No, the reduced echelon form of the augmented matrix is, which is an inconsistent system.
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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![### Linear Algebra: Vector and Matrix Subset Question
#### Problem Statement:
Let \( \mathbf{u} = \begin{bmatrix} 0 \\ 6 \\ -1 \end{bmatrix} \) and \( A = \begin{bmatrix} 4 & 8 & 4 \\ 1 & 0 & 3 \\ 1 & 2 & 1 \end{bmatrix} \). Is \( \mathbf{u} \) in the subset of \( \mathbb{R}^3 \) spanned by the columns of \( A \)? Why or why not?
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#### Problem Response:
Select the correct choice below and fill in the answer box to complete your choice.
*(Type an integer or decimal for each matrix element.)*
- [ ] **A.** Yes, multiplying \( A \) by the vector \(\begin{bmatrix} \_\_ \\ \_\_ \\ \_\_ \end{bmatrix}\) writes \( \mathbf{u} \) as a linear combination of the columns of \( A \).
- [ ] **B.** No, the reduced echelon form of the augmented matrix is \(\begin{bmatrix} \_\_ & \_\_ & \_\_ & \_\_ \\ \_\_ & \_\_ & \_\_ & \_\_ \\ \_\_ & \_\_ & \_\_ & \_\_ \end{bmatrix}\), which is an inconsistent system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70fe4f99-9e69-4bef-afe6-80d54e8903ee%2F176c8e76-dbb1-4f0a-857f-aaf87c3ffe43%2Fn1vjoem_processed.png&w=3840&q=75)
Transcribed Image Text:### Linear Algebra: Vector and Matrix Subset Question
#### Problem Statement:
Let \( \mathbf{u} = \begin{bmatrix} 0 \\ 6 \\ -1 \end{bmatrix} \) and \( A = \begin{bmatrix} 4 & 8 & 4 \\ 1 & 0 & 3 \\ 1 & 2 & 1 \end{bmatrix} \). Is \( \mathbf{u} \) in the subset of \( \mathbb{R}^3 \) spanned by the columns of \( A \)? Why or why not?
---
#### Problem Response:
Select the correct choice below and fill in the answer box to complete your choice.
*(Type an integer or decimal for each matrix element.)*
- [ ] **A.** Yes, multiplying \( A \) by the vector \(\begin{bmatrix} \_\_ \\ \_\_ \\ \_\_ \end{bmatrix}\) writes \( \mathbf{u} \) as a linear combination of the columns of \( A \).
- [ ] **B.** No, the reduced echelon form of the augmented matrix is \(\begin{bmatrix} \_\_ & \_\_ & \_\_ & \_\_ \\ \_\_ & \_\_ & \_\_ & \_\_ \\ \_\_ & \_\_ & \_\_ & \_\_ \end{bmatrix}\), which is an inconsistent system.
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