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indi dove krem In Exercises 7-10, let B = {b₁,b2} and C = {C₁, C₂} be bases for R². In each exercise, find the change-of-coordinates matrix from B to C and the change-of-coordinates matrix from C to B.

indi dove krem In Exercises 7-10, let B = {b₁,b2} and C = {C₁, C₂} be bases for R². In each exercise, find the change-of-coordinates matrix from B to C and the change-of-coordinates matrix from C to B.

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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In Exercises 7-10, let \(\mathcal{B} = \{\mathbf{b}_1, \mathbf{b}_2\}\) and \(\mathcal{C} = \{\mathbf{c}_1, \mathbf{c}_2\}\) be bases for \(\mathbb{R}^2\). In each exercise, find the change-of-coordinates matrix from \(\mathcal{B}\) to \(\mathcal{C}\) and the change-of-coordinates matrix from \(\mathcal{C}\) to \(\mathcal{B}\).
Transcribed Image Text:In Exercises 7-10, let \(\mathcal{B} = \{\mathbf{b}_1, \mathbf{b}_2\}\) and \(\mathcal{C} = \{\mathbf{c}_1, \mathbf{c}_2\}\) be bases for \(\mathbb{R}^2\). In each exercise, find the change-of-coordinates matrix from \(\mathcal{B}\) to \(\mathcal{C}\) and the change-of-coordinates matrix from \(\mathcal{C}\) to \(\mathcal{B}\).
10. \(\mathbf{b}_1 = \begin{bmatrix} 7 \\ -2 \end{bmatrix}, \mathbf{b}_2 = \begin{bmatrix} 2 \\ -1 \end{bmatrix}, \mathbf{c}_1 = \begin{bmatrix} 4 \\ 1 \end{bmatrix}, \mathbf{c}_2 = \begin{bmatrix} 5 \\ 2 \end{bmatrix}\)
Transcribed Image Text:10. \(\mathbf{b}_1 = \begin{bmatrix} 7 \\ -2 \end{bmatrix}, \mathbf{b}_2 = \begin{bmatrix} 2 \\ -1 \end{bmatrix}, \mathbf{c}_1 = \begin{bmatrix} 4 \\ 1 \end{bmatrix}, \mathbf{c}_2 = \begin{bmatrix} 5 \\ 2 \end{bmatrix}\)
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