4 1 ---[[]] } = span ' 2 2 Let H Determine a basis for H which consists of a subset of the given vectors. { }
4 1 ---[[]] } = span ' 2 2 Let H Determine a basis for H which consists of a subset of the given vectors. { }
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
![Let \( H = \text{span} \left\{ \begin{bmatrix} 2 \\ 4 \\ 6 \\ -6 \end{bmatrix}, \begin{bmatrix} 0 \\ 1 \\ 2 \\ -2 \end{bmatrix}, \begin{bmatrix} 0 \\ 1 \\ 1 \\ -1 \end{bmatrix}, \begin{bmatrix} -1 \\ -1 \\ -2 \\ 2 \end{bmatrix} \right\}. \)
Determine a basis for \( H \) which consists of a subset of the given vectors:
\[
\left\{ \begin{bmatrix} \boxed{} \\ \boxed{} \\ \boxed{} \\ \boxed{} \end{bmatrix}, \begin{bmatrix} \boxed{} \\ \boxed{} \\ \boxed{} \\ \boxed{} \end{bmatrix}, \begin{bmatrix} \boxed{} \\ \boxed{} \\ \boxed{} \\ \boxed{} \end{bmatrix} \right\}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c49f70f-02c0-4076-b0a5-564b9a6f1d8d%2F1a104641-fe07-4a78-be1a-9b8c9250ff60%2Fvtgcqkt_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( H = \text{span} \left\{ \begin{bmatrix} 2 \\ 4 \\ 6 \\ -6 \end{bmatrix}, \begin{bmatrix} 0 \\ 1 \\ 2 \\ -2 \end{bmatrix}, \begin{bmatrix} 0 \\ 1 \\ 1 \\ -1 \end{bmatrix}, \begin{bmatrix} -1 \\ -1 \\ -2 \\ 2 \end{bmatrix} \right\}. \)
Determine a basis for \( H \) which consists of a subset of the given vectors:
\[
\left\{ \begin{bmatrix} \boxed{} \\ \boxed{} \\ \boxed{} \\ \boxed{} \end{bmatrix}, \begin{bmatrix} \boxed{} \\ \boxed{} \\ \boxed{} \\ \boxed{} \end{bmatrix}, \begin{bmatrix} \boxed{} \\ \boxed{} \\ \boxed{} \\ \boxed{} \end{bmatrix} \right\}
\]
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