Let B = {b₁,b2, b3} be a basis of R³ where Find the vector V. b₁ Enter the vector V in the form [C1, C2, C3]: = b₂ = [ 3 Let v be a vector in R³ such that coordinates of v relative to the basis Bare given by 2 -H -3 2 [V] B = b3 = 4 4
Let B = {b₁,b2, b3} be a basis of R³ where Find the vector V. b₁ Enter the vector V in the form [C1, C2, C3]: = b₂ = [ 3 Let v be a vector in R³ such that coordinates of v relative to the basis Bare given by 2 -H -3 2 [V] B = b3 = 4 4
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 \(\mathcal{B} = \{\mathbf{b_1}, \mathbf{b_2}, \mathbf{b_3}\}\) be a basis of \(\mathbb{R}^3\) where
\[
\mathbf{b_1} = \begin{bmatrix} -1 \\ 5 \\ 3 \end{bmatrix} \quad \mathbf{b_2} = \begin{bmatrix} 2 \\ 2 \\ 5 \end{bmatrix} \quad \mathbf{b_3} = \begin{bmatrix} 4 \\ 4 \\ -1 \end{bmatrix}
\]
Let \(\mathbf{v}\) be a vector in \(\mathbb{R}^3\) such that coordinates of \(\mathbf{v}\) relative to the basis \(\mathcal{B}\) are given by
\[
[\mathbf{v}]_{\mathcal{B}} = \begin{bmatrix} 2 \\ -3 \\ -2 \end{bmatrix}
\]
Find the vector \(\mathbf{v}\).
Enter the vector \(\mathbf{v}\) in the form \([\mathbf{c_1}, \mathbf{c_2}, \mathbf{c_3}]\):](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb493ecdd-cbdc-400d-a05a-de2010eb2d52%2Ffc6efbca-115c-4d78-bbef-63134672c34e%2F1sepujr_processed.png&w=3840&q=75)
Transcribed Image Text:Let \(\mathcal{B} = \{\mathbf{b_1}, \mathbf{b_2}, \mathbf{b_3}\}\) be a basis of \(\mathbb{R}^3\) where
\[
\mathbf{b_1} = \begin{bmatrix} -1 \\ 5 \\ 3 \end{bmatrix} \quad \mathbf{b_2} = \begin{bmatrix} 2 \\ 2 \\ 5 \end{bmatrix} \quad \mathbf{b_3} = \begin{bmatrix} 4 \\ 4 \\ -1 \end{bmatrix}
\]
Let \(\mathbf{v}\) be a vector in \(\mathbb{R}^3\) such that coordinates of \(\mathbf{v}\) relative to the basis \(\mathcal{B}\) are given by
\[
[\mathbf{v}]_{\mathcal{B}} = \begin{bmatrix} 2 \\ -3 \\ -2 \end{bmatrix}
\]
Find the vector \(\mathbf{v}\).
Enter the vector \(\mathbf{v}\) in the form \([\mathbf{c_1}, \mathbf{c_2}, \mathbf{c_3}]\):
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