Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

Solve this multiple choice linear algebra question, please whoe your work. 

**Determine if the vectors** \[ \begin{bmatrix} 2 \\ -2 \\ 1 \end{bmatrix}, \begin{bmatrix} 1 \\ -3 \\ 2 \end{bmatrix}, \text{ and }\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} \] **are linearly dependent or independent. Also determine if the vectors span** \( \mathbb{R}^3 \) **or not.** **Options:** - ☐ The vectors are linearly dependent and they do not span \( \mathbb{R}^3 \). - ☐ The vectors are linearly dependent and they span \( \mathbb{R}^3 \). - ☐ The vectors are linearly independent and they span \( \mathbb{R}^3 \). They form a basis for \( \mathbb{R}^3 \). - ☐ The vectors are linearly independent and they do not span \( \mathbb{R}^3 \).
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Transcribed Image Text:**Determine if the vectors** \[ \begin{bmatrix} 2 \\ -2 \\ 1 \end{bmatrix}, \begin{bmatrix} 1 \\ -3 \\ 2 \end{bmatrix}, \text{ and }\begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} \] **are linearly dependent or independent. Also determine if the vectors span** \( \mathbb{R}^3 \) **or not.** **Options:** - ☐ The vectors are linearly dependent and they do not span \( \mathbb{R}^3 \). - ☐ The vectors are linearly dependent and they span \( \mathbb{R}^3 \). - ☐ The vectors are linearly independent and they span \( \mathbb{R}^3 \). They form a basis for \( \mathbb{R}^3 \). - ☐ The vectors are linearly independent and they do not span \( \mathbb{R}^3 \).
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