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2 Let B= 3. 2 -1 be a basis of R³ and let x = 5 -1 4 be a vector

2 Let B= 3. 2 -1 be a basis of R³ and let x = 5 -1 4 be a vector

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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**Exercise 10.4.2** Let \( B = \left\{ \begin{bmatrix} 1 \\ -1 \\ 2 \end{bmatrix}, \begin{bmatrix} 2 \\ 1 \\ 2 \end{bmatrix}, \begin{bmatrix} -1 \\ 0 \\ 2 \end{bmatrix} \right\} \) be a basis of \( \mathbb{R}^3 \) and let \( \mathbf{x} = \begin{bmatrix} 5 \\ -1 \\ 4 \end{bmatrix} \) be a vector in \( \mathbb{R}^3 \). Find \( [\mathbf{x}]_B \).
Transcribed Image Text:**Exercise 10.4.2** Let \( B = \left\{ \begin{bmatrix} 1 \\ -1 \\ 2 \end{bmatrix}, \begin{bmatrix} 2 \\ 1 \\ 2 \end{bmatrix}, \begin{bmatrix} -1 \\ 0 \\ 2 \end{bmatrix} \right\} \) be a basis of \( \mathbb{R}^3 \) and let \( \mathbf{x} = \begin{bmatrix} 5 \\ -1 \\ 4 \end{bmatrix} \) be a vector in \( \mathbb{R}^3 \). Find \( [\mathbf{x}]_B \).
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