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Determine if the set of vectors shown to the right is a basis for R³. If the set of vectors is not a basis, determine whether it is linearly independent and whether the set spans R³. Which of the following describe the set? Select all that apply. A. The set is a basis for R³. B. The set is linearly independent. C. The set spans R³. D. None of the above 3 2 GO -4 1 2 - 9 6 3

Determine if the set of vectors shown to the right is a basis for R³. If the set of vectors is not a basis, determine whether it is linearly independent and whether the set spans R³. Which of the following describe the set? Select all that apply. A. The set is a basis for R³. B. The set is linearly independent. C. The set spans R³. D. None of the above 3 2 GO -4 1 2 - 9 6 3

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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### Determine Basis and Linear Independence Determine if the set of vectors shown to the right is a basis for \(\mathbb{R}^3\). If the set of vectors is not a basis, determine whether it is linearly independent and whether the set spans \(\mathbb{R}^3\). \[ \left\{ \begin{bmatrix} 3 \\ -1 \\ 1 \end{bmatrix}, \begin{bmatrix} 2 \\ -4 \\ 2 \end{bmatrix}, \begin{bmatrix} -9 \\ 6 \\ 3 \end{bmatrix} \right\} \] --- ### Multiple Choice Question Which of the following describe the set? Select all that apply. - [ ] A. The set is a basis for \(\mathbb{R}^3\). - [ ] B. The set is linearly independent. - [ ] C. The set spans \(\mathbb{R}^3\). - [ ] D. None of the above --- To solve the question, analyze if the given vectors are linearly independent and if they span the vector space \(\mathbb{R}^3\). A set of three vectors is a basis for \(\mathbb{R}^3\) if it is linearly independent and spans \(\mathbb{R}^3\).
Transcribed Image Text:### Determine Basis and Linear Independence Determine if the set of vectors shown to the right is a basis for \(\mathbb{R}^3\). If the set of vectors is not a basis, determine whether it is linearly independent and whether the set spans \(\mathbb{R}^3\). \[ \left\{ \begin{bmatrix} 3 \\ -1 \\ 1 \end{bmatrix}, \begin{bmatrix} 2 \\ -4 \\ 2 \end{bmatrix}, \begin{bmatrix} -9 \\ 6 \\ 3 \end{bmatrix} \right\} \] --- ### Multiple Choice Question Which of the following describe the set? Select all that apply. - [ ] A. The set is a basis for \(\mathbb{R}^3\). - [ ] B. The set is linearly independent. - [ ] C. The set spans \(\mathbb{R}^3\). - [ ] D. None of the above --- To solve the question, analyze if the given vectors are linearly independent and if they span the vector space \(\mathbb{R}^3\). A set of three vectors is a basis for \(\mathbb{R}^3\) if it is linearly independent and spans \(\mathbb{R}^3\).
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