ind the coordinate vector [x]g of x relative to the given basis B= (by, by by) b₁ = -1,b₂ = -4 -3 2 4, b3 = -2 12 4 X= 5
ind the coordinate vector [x]g of x relative to the given basis B= (by, by by) b₁ = -1,b₂ = -4 -3 2 4, b3 = -2 12 4 X= 5
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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![Find the coordinate vector \([x]_B\) of \(x\) relative to the given basis \(B = \{b_1, b_2, b_3\}\).
\[
b_1 = \begin{bmatrix} 1 \\ -1 \\ -4 \end{bmatrix}, \quad
b_2 = \begin{bmatrix} -3 \\ 4 \\ 12 \end{bmatrix}, \quad
b_3 = \begin{bmatrix} 2 \\ -2 \\ 4 \end{bmatrix}, \quad
x = \begin{bmatrix} -4 \\ 5 \\ 4 \end{bmatrix}
\]
\[ [x]_B = \Box \]
(Simplify your answer.)
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Transcribed Image Text:Find the coordinate vector \([x]_B\) of \(x\) relative to the given basis \(B = \{b_1, b_2, b_3\}\).
\[
b_1 = \begin{bmatrix} 1 \\ -1 \\ -4 \end{bmatrix}, \quad
b_2 = \begin{bmatrix} -3 \\ 4 \\ 12 \end{bmatrix}, \quad
b_3 = \begin{bmatrix} 2 \\ -2 \\ 4 \end{bmatrix}, \quad
x = \begin{bmatrix} -4 \\ 5 \\ 4 \end{bmatrix}
\]
\[ [x]_B = \Box \]
(Simplify your answer.)
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