) Let 1 3 2 -2 1 -2 2 8 6. be given vectors in R³. Determine if b is a linear combination of v1, v2 and iz.
) Let 1 3 2 -2 1 -2 2 8 6. be given vectors in R³. Determine if b is a linear combination of v1, v2 and iz.
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
![Let
\[
\mathbf{v}_1 = \begin{bmatrix} 1 \\ -2 \\ 0 \end{bmatrix}, \quad \mathbf{v}_2 = \begin{bmatrix} 0 \\ 1 \\ 2 \end{bmatrix}, \quad \mathbf{v}_3 = \begin{bmatrix} 3 \\ -2 \\ 8 \end{bmatrix}, \quad \mathbf{b} = \begin{bmatrix} 2 \\ -1 \\ 6 \end{bmatrix}
\]
be given vectors in \( \mathbb{R}^3 \). Determine if \( \mathbf{b} \) is a linear combination of \( \mathbf{v}_1 \), \( \mathbf{v}_2 \), and \( \mathbf{v}_3 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F734f4932-9c15-4e07-80c9-d54d94f3ad88%2F65a0079f-7319-4478-85ed-a9a3e7917b76%2Fpw4hld_processed.png&w=3840&q=75)
Transcribed Image Text:Let
\[
\mathbf{v}_1 = \begin{bmatrix} 1 \\ -2 \\ 0 \end{bmatrix}, \quad \mathbf{v}_2 = \begin{bmatrix} 0 \\ 1 \\ 2 \end{bmatrix}, \quad \mathbf{v}_3 = \begin{bmatrix} 3 \\ -2 \\ 8 \end{bmatrix}, \quad \mathbf{b} = \begin{bmatrix} 2 \\ -1 \\ 6 \end{bmatrix}
\]
be given vectors in \( \mathbb{R}^3 \). Determine if \( \mathbf{b} \) is a linear combination of \( \mathbf{v}_1 \), \( \mathbf{v}_2 \), and \( \mathbf{v}_3 \).
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