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Pick every true statement which applies to the following set of vectors. {8·4)} O This set spans R^3 O Every vector in its span can be written uniquely as a linear combination of these vectors O This set of vectors is linearly dependent O This set is a basis of R^3 O None of the above answers are true

Pick every true statement which applies to the following set of vectors. {8·4)} O This set spans R^3 O Every vector in its span can be written uniquely as a linear combination of these vectors O This set of vectors is linearly dependent O This set is a basis of R^3 O None of the above answers are true

Advanced Engineering Mathematics
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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**Question: Pick every true statement which applies to the following set of vectors.** \[ \left\{ \begin{pmatrix} 1 \\ 0 \\ 3 \end{pmatrix}, \begin{pmatrix} 2 \\ -1 \\ 0 \end{pmatrix} \right\} \] - [ ] This set spans \(\mathbb{R}^3\) - [ ] Every vector in its span can be written uniquely as a linear combination of these vectors - [ ] This set of vectors is linearly dependent - [ ] This set is a basis of \(\mathbb{R}^3\) - [ ] None of the above answers are true
Transcribed Image Text:**Question: Pick every true statement which applies to the following set of vectors.** \[ \left\{ \begin{pmatrix} 1 \\ 0 \\ 3 \end{pmatrix}, \begin{pmatrix} 2 \\ -1 \\ 0 \end{pmatrix} \right\} \] - [ ] This set spans \(\mathbb{R}^3\) - [ ] Every vector in its span can be written uniquely as a linear combination of these vectors - [ ] This set of vectors is linearly dependent - [ ] This set is a basis of \(\mathbb{R}^3\) - [ ] None of the above answers are true
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