3 aj = 4 a2 = 9 az = -3 b = 2 Determine if vector b is a linear combination of a1, a2, and a3. Show all your work, do not skip steps. Displaying only the final answer is not enough to get credit.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Determine if vector \( \mathbf{b} \) is a linear combination of \( \mathbf{a_1} \), \( \mathbf{a_2} \), and \( \mathbf{a_3} \).**

\[ \mathbf{a_1} = \begin{pmatrix} -1 \\ 4 \\ -3 \end{pmatrix}; \mathbf{a_2} = \begin{pmatrix} -2 \\ 9 \\ -7 \end{pmatrix}; \mathbf{a_3} = \begin{pmatrix} 1 \\ -3 \\ 2 \end{pmatrix}; \mathbf{b} = \begin{pmatrix} 3 \\ -1 \\ 2 \end{pmatrix} \]

Show all your work, do not skip steps. Displaying only the final answer is not enough to get credit.

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## Solution

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Transcribed Image Text:**Determine if vector \( \mathbf{b} \) is a linear combination of \( \mathbf{a_1} \), \( \mathbf{a_2} \), and \( \mathbf{a_3} \).** \[ \mathbf{a_1} = \begin{pmatrix} -1 \\ 4 \\ -3 \end{pmatrix}; \mathbf{a_2} = \begin{pmatrix} -2 \\ 9 \\ -7 \end{pmatrix}; \mathbf{a_3} = \begin{pmatrix} 1 \\ -3 \\ 2 \end{pmatrix}; \mathbf{b} = \begin{pmatrix} 3 \\ -1 \\ 2 \end{pmatrix} \] Show all your work, do not skip steps. Displaying only the final answer is not enough to get credit. --- ## Solution *(Show all intermediate steps, formulas, calculations, explanations, and comments below this line. Don't write above this line)*
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