1 0 1 ~EHEMMEHO V 4 2 0 Let v = 1 0 4 O C.S O d. {v, - and S= { v₁ O a. (v. v₂} 1 2 9 O b. {V₁, V 3 } 1 v₁} 4 . 1 1 V 3 4 ○e. { v₁ • V 2• V3} 0 0 and v }. A basis for span (S) is 4 1 1 6
1 0 1 ~EHEMMEHO V 4 2 0 Let v = 1 0 4 O C.S O d. {v, - and S= { v₁ O a. (v. v₂} 1 2 9 O b. {V₁, V 3 } 1 v₁} 4 . 1 1 V 3 4 ○e. { v₁ • V 2• V3} 0 0 and v }. A basis for span (S) is 4 1 1 6
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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![The image contains mathematical text and a problem related to linear algebra. Here is the transcription:
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**Let** \( v_1 = \begin{bmatrix} 1 \\ 0 \\ 4 \\ -1 \end{bmatrix} = \begin{bmatrix} 1 \\ 0 \\ 4 \\ -1 \end{bmatrix}, \quad v_2 = \begin{bmatrix} 1 \\ 0 \\ 2 \\ -1 \end{bmatrix}, \quad v_3 = \begin{bmatrix} -1 \\ 0 \\ 0 \\ -1 \end{bmatrix} \quad \text{and} \quad v_4 = \begin{bmatrix} 1 \\ 1 \\ 6 \\ -2 \end{bmatrix} \]
and \( S = \{ v_1, v_2, v_3, v_4 \} \). A basis for span(\( S \)) is
- a. \( \{ v_1, v_2 \} \)
- b. \( \{ v_1, v_3 \} \)
- c. \( S \)
- d. \( \{ v_1, v_4 \} \)
- e. \( \{ v_1, v_2, v_3 \} \)
---
This section is designed for educational purposes to explore the concept of vector spaces and basis determination in linear algebra.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c49f70f-02c0-4076-b0a5-564b9a6f1d8d%2F97922e56-7736-4dfe-b76d-bf94ad1a17d4%2Fn8psmnm_processed.png&w=3840&q=75)
Transcribed Image Text:The image contains mathematical text and a problem related to linear algebra. Here is the transcription:
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**Let** \( v_1 = \begin{bmatrix} 1 \\ 0 \\ 4 \\ -1 \end{bmatrix} = \begin{bmatrix} 1 \\ 0 \\ 4 \\ -1 \end{bmatrix}, \quad v_2 = \begin{bmatrix} 1 \\ 0 \\ 2 \\ -1 \end{bmatrix}, \quad v_3 = \begin{bmatrix} -1 \\ 0 \\ 0 \\ -1 \end{bmatrix} \quad \text{and} \quad v_4 = \begin{bmatrix} 1 \\ 1 \\ 6 \\ -2 \end{bmatrix} \]
and \( S = \{ v_1, v_2, v_3, v_4 \} \). A basis for span(\( S \)) is
- a. \( \{ v_1, v_2 \} \)
- b. \( \{ v_1, v_3 \} \)
- c. \( S \)
- d. \( \{ v_1, v_4 \} \)
- e. \( \{ v_1, v_2, v_3 \} \)
---
This section is designed for educational purposes to explore the concept of vector spaces and basis determination in linear algebra.
Transcribed Image Text:Select all subspaces of \(\mathbb{R}^3\).
a. \(\begin{bmatrix} 1 & 3 \\ 0 & 1 \\ 2 & 7 \end{bmatrix}\)
\(col\left(\begin{bmatrix} 1 & 3 \\ 0 & 1 \\ 2 & 7 \end{bmatrix}\right)\)
b. \(\{(x + 2, x - 1, z) \, / \, x \text{ and } z \text{ are arbitrary real numbers}\}\)
c. \(\begin{pmatrix} 3 \\ 0 \\ 1 \end{pmatrix}\)
\(span\left\{\begin{pmatrix} 3 \\ 0 \\ 1 \end{pmatrix}\right\}\)
d. \(\{(2x, 3x, 4x) \, / \, x \in \mathbb{R} \}\)
e. \(\{(x, y, z) \in \mathbb{R}^3 \, / \, x + y + z = 0 \}\)
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