6 B *- {[1][*]} [6]. -- 6 [3] is an orthogonal basis of R². Find [v]®•
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
![The problem presents an orthogonal basis for \( \mathbb{R}^2 \), denoted as:
\[
\mathcal{B} = \left\{ \begin{bmatrix} 6 \\ 6 \end{bmatrix}, \begin{bmatrix} 6 \\ -6 \end{bmatrix} \right\}
\]
and asks to find the coordinates of the vector \( \mathbf{v} \) with respect to this basis. The vector \( \mathbf{v} \) is given by:
\[
\mathbf{v} = \begin{bmatrix} 6 \\ 3 \end{bmatrix}
\]
The task is to find \([\mathbf{v}]_{\mathcal{B}}\), the representation of the vector \( \mathbf{v} \) in the basis \(\mathcal{B}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F807728d5-81cc-4dac-b6a1-9785980c085b%2Fe77dfbd8-5865-4a16-b4c0-40bca8d78f5f%2Fftwqie_processed.png&w=3840&q=75)
Transcribed Image Text:The problem presents an orthogonal basis for \( \mathbb{R}^2 \), denoted as:
\[
\mathcal{B} = \left\{ \begin{bmatrix} 6 \\ 6 \end{bmatrix}, \begin{bmatrix} 6 \\ -6 \end{bmatrix} \right\}
\]
and asks to find the coordinates of the vector \( \mathbf{v} \) with respect to this basis. The vector \( \mathbf{v} \) is given by:
\[
\mathbf{v} = \begin{bmatrix} 6 \\ 3 \end{bmatrix}
\]
The task is to find \([\mathbf{v}]_{\mathcal{B}}\), the representation of the vector \( \mathbf{v} \) in the basis \(\mathcal{B}\).
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