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Part I: Consider the subspace of M2x2 that has [23] 32 is the coordinate vector of Part II: What matrix has 4 {[1]} with respect to this basis? as its coordinate vector? as an ordered basis. What

Part I: Consider the subspace of M2x2 that has [23] 32 is the coordinate vector of Part II: What matrix has 4 {[1]} with respect to this basis? as its coordinate vector? as an ordered basis. What

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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**Part I:** Consider the subspace of \( M_{2 \times 2} \) that has \( \left\{ \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}, \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \right\} \) as an ordered basis. What is the coordinate vector of \( \begin{bmatrix} 2 & 3 \\ 3 & 2 \end{bmatrix} \) with respect to this basis? **Part II:** What matrix has \( \begin{bmatrix} 1 \\ -1 \end{bmatrix} \) as its coordinate vector?
Transcribed Image Text:**Part I:** Consider the subspace of \( M_{2 \times 2} \) that has \( \left\{ \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}, \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \right\} \) as an ordered basis. What is the coordinate vector of \( \begin{bmatrix} 2 & 3 \\ 3 & 2 \end{bmatrix} \) with respect to this basis? **Part II:** What matrix has \( \begin{bmatrix} 1 \\ -1 \end{bmatrix} \) as its coordinate vector?
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