20. 1 -5 3 5 4 v₁ - 3v₂ +5v3 = 0. Use this information to find a basis for H = Span {V₁, V2, V3}. Let V1 = 7 4 -9 , V2 = 4 -7 2 , V3 = . It can be verified that
20. 1 -5 3 5 4 v₁ - 3v₂ +5v3 = 0. Use this information to find a basis for H = Span {V₁, V2, V3}. Let V1 = 7 4 -9 , V2 = 4 -7 2 , V3 = . It can be verified that
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: Finding a Basis
#### Problem 20
Given the vectors:
\[ \mathbf{v}_1 = \begin{bmatrix} 7 \\ 4 \\ -9 \\ -5 \end{bmatrix}, \quad \mathbf{v}_2 = \begin{bmatrix} 4 \\ -7 \\ 2 \\ 5 \end{bmatrix}, \quad \mathbf{v}_3 = \begin{bmatrix} 1 \\ -5 \\ 3 \\ 4 \end{bmatrix} \]
It can be verified that:
\[ \mathbf{v}_1 - 3\mathbf{v}_2 + 5\mathbf{v}_3 = 0 \]
Using this information, find a basis for the subspace \( H = \text{Span} \{\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3\} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F324f16c4-c4e5-4b06-b074-f261b39e021a%2Fddbc60df-637c-45c9-b6b4-15b9c508b1cc%2Fxa7nglk_processed.png&w=3840&q=75)
Transcribed Image Text:### Linear Algebra: Finding a Basis
#### Problem 20
Given the vectors:
\[ \mathbf{v}_1 = \begin{bmatrix} 7 \\ 4 \\ -9 \\ -5 \end{bmatrix}, \quad \mathbf{v}_2 = \begin{bmatrix} 4 \\ -7 \\ 2 \\ 5 \end{bmatrix}, \quad \mathbf{v}_3 = \begin{bmatrix} 1 \\ -5 \\ 3 \\ 4 \end{bmatrix} \]
It can be verified that:
\[ \mathbf{v}_1 - 3\mathbf{v}_2 + 5\mathbf{v}_3 = 0 \]
Using this information, find a basis for the subspace \( H = \text{Span} \{\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3\} \).
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