Let B= = : {b₁, b₂} and C = {c₁, c₂} be bases for a vector space V, and suppose V = b₁ b2 = [v] = [B\C [v]ε] = 7b₁ + 4b2 -C1 +9c₂ 7c₁
Let B= = : {b₁, b₂} and C = {c₁, c₂} be bases for a vector space V, and suppose V = b₁ b2 = [v] = [B\C [v]ε] = 7b₁ + 4b2 -C1 +9c₂ 7c₁
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 \( \mathcal{B} = \{\mathbf{b_1}, \mathbf{b_2}\} \) and \( \mathcal{C} = \{\mathbf{c_1}, \mathbf{c_2}\} \) be bases for a vector space \( V \), and suppose
\[
\mathbf{v} = 7\mathbf{b_1} + 4\mathbf{b_2}
\]
\[
\mathbf{b_1} = -\mathbf{c_1} + 9\mathbf{c_2}
\]
\[
\mathbf{b_2} = 7\mathbf{c_1}
\]
\[
[\mathbf{v}]_{\mathcal{B}} = \boxed{}
\]
\[
[\mathcal{B}]_{\mathcal{C}} = \boxed{}
\]
\[
[\mathbf{v}]_{\mathcal{C}} = \boxed{}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b87c16f-5797-4fee-9867-0be2bea00aaa%2F7012ca57-5227-4e15-a3f0-cb486cddcef0%2Fhzaamjd_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( \mathcal{B} = \{\mathbf{b_1}, \mathbf{b_2}\} \) and \( \mathcal{C} = \{\mathbf{c_1}, \mathbf{c_2}\} \) be bases for a vector space \( V \), and suppose
\[
\mathbf{v} = 7\mathbf{b_1} + 4\mathbf{b_2}
\]
\[
\mathbf{b_1} = -\mathbf{c_1} + 9\mathbf{c_2}
\]
\[
\mathbf{b_2} = 7\mathbf{c_1}
\]
\[
[\mathbf{v}]_{\mathcal{B}} = \boxed{}
\]
\[
[\mathcal{B}]_{\mathcal{C}} = \boxed{}
\]
\[
[\mathbf{v}]_{\mathcal{C}} = \boxed{}
\]
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