Consider the following vectors in R5: 5 12 7 -7 -11 Find a basis of Span (V1, V2, V3, V4, V5). For convenience, here is the above list of vectors in a form that can be copied into Python code: V1 = V2 = 10 24 14 -14 -22 Hint. Notice that Span (V1, V2, V3, V4, V5): = V3 7 6 -3 -3 0 -1 , V4= 1 13 -1 5 " Col (A) where Col (A) = [V₁ V2 V3 V4 V5]. V5 = -7 -9 [5,12,7,-7, -11], [10, 24, 14, -14, -22], [7,6,-1,1,-13], [-3, -3,0,-1,5], [-7,-9, -2,1,13] -2 1 13
Consider the following vectors in R5: 5 12 7 -7 -11 Find a basis of Span (V1, V2, V3, V4, V5). For convenience, here is the above list of vectors in a form that can be copied into Python code: V1 = V2 = 10 24 14 -14 -22 Hint. Notice that Span (V1, V2, V3, V4, V5): = V3 7 6 -3 -3 0 -1 , V4= 1 13 -1 5 " Col (A) where Col (A) = [V₁ V2 V3 V4 V5]. V5 = -7 -9 [5,12,7,-7, -11], [10, 24, 14, -14, -22], [7,6,-1,1,-13], [-3, -3,0,-1,5], [-7,-9, -2,1,13] -2 1 13
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Consider the following vectors in \( \mathbb{R}^5 \):
\[
\mathbf{v}_1 = \begin{bmatrix} 5 \\ 12 \\ 7 \\ -7 \\ -11 \end{bmatrix}, \quad \mathbf{v}_2 = \begin{bmatrix} 10 \\ 24 \\ 14 \\ -14 \\ -22 \end{bmatrix}, \quad \mathbf{v}_3 = \begin{bmatrix} 7 \\ 6 \\ -1 \\ 1 \\ -13 \end{bmatrix}, \quad \mathbf{v}_4 = \begin{bmatrix} -3 \\ -3 \\ 0 \\ -1 \\ 5 \end{bmatrix}, \quad \mathbf{v}_5 = \begin{bmatrix} -7 \\ -9 \\ -2 \\ 1 \\ 13 \end{bmatrix}
\]
Find a basis of \(\text{Span}(\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3, \mathbf{v}_4, \mathbf{v}_5)\).
For convenience, here is the above list of vectors in a form that can be copied into Python code:
```
[5,12,7,-7,-11],[10,24,14,-14,-22],[7,6,-1,1,-13],[-3,-3,0,-1,5],[-7,-9,-2,1,13]
```
**Hint.** Notice that \(\text{Span}(\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3, \mathbf{v}_4, \mathbf{v}_5) = \text{Col}(A)\) where \(\text{Col}(A) = [\mathbf{v}_1 \ \mathbf{v}_2 \ \mathbf{v}_3 \ \mathbf{v}_4 \ \mathbf{v}_5]\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb493ecdd-cbdc-400d-a05a-de2010eb2d52%2Fbb04e449-6be6-4885-9124-f61feb914ff2%2Fho8e7s5_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following vectors in \( \mathbb{R}^5 \):
\[
\mathbf{v}_1 = \begin{bmatrix} 5 \\ 12 \\ 7 \\ -7 \\ -11 \end{bmatrix}, \quad \mathbf{v}_2 = \begin{bmatrix} 10 \\ 24 \\ 14 \\ -14 \\ -22 \end{bmatrix}, \quad \mathbf{v}_3 = \begin{bmatrix} 7 \\ 6 \\ -1 \\ 1 \\ -13 \end{bmatrix}, \quad \mathbf{v}_4 = \begin{bmatrix} -3 \\ -3 \\ 0 \\ -1 \\ 5 \end{bmatrix}, \quad \mathbf{v}_5 = \begin{bmatrix} -7 \\ -9 \\ -2 \\ 1 \\ 13 \end{bmatrix}
\]
Find a basis of \(\text{Span}(\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3, \mathbf{v}_4, \mathbf{v}_5)\).
For convenience, here is the above list of vectors in a form that can be copied into Python code:
```
[5,12,7,-7,-11],[10,24,14,-14,-22],[7,6,-1,1,-13],[-3,-3,0,-1,5],[-7,-9,-2,1,13]
```
**Hint.** Notice that \(\text{Span}(\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3, \mathbf{v}_4, \mathbf{v}_5) = \text{Col}(A)\) where \(\text{Col}(A) = [\mathbf{v}_1 \ \mathbf{v}_2 \ \mathbf{v}_3 \ \mathbf{v}_4 \ \mathbf{v}_5]\).
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