Question 1: Consider the subspace of M2x2 that has {2 33 2What is the coordinate vector ofQuestion 2: What matrix has10[16] } as an ordered basis.4with respect to this basis?as its coordinate vector?

Answered: Image /qna-images/answer/c7827120-1ed6-4b82-ab4f-705284102d42.jpg

Answered: Question 1: Consider the subspace of…

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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The standard basis & (e₁,e₂) and two custom bases B (b₁,b₂} and C (c₁, c₂} for R² are shown in the figures below. Standard basis S= (₁, ₂) 4 a. Find the change of basis matrix from custom B-coordinates to standard S-coordinates. [id] = id= -2 b Find the change of basis matrix from custom C-coordinates to standard S-coordinates [id] = -1 -1 -1 c. Find the change of basis matrix from B-coordinates to C-coordinates -3 -1/12 1/4 d. Find the change of basis matrix from C-coordinates to B-coordinates. 3 2 1 -1 -2 -9 b2 -3-2-1 82 el bl 1 2 3 b1 X Custom basis B = {b₁,b₂) |id|s [id Standard basis S= (0₁,0₂} a 3 2 1 -1 -2 -9 c2 -3 -2 -1 G2 62 217 el [id] ↑ cl 12 2 3 61 H x Custom basis C (C₁, C₂)
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Question 1: Consider the subspace of M2×2 that has { 1 [01] $11 with respect to this basis? What is the coordinate vector of Question 2: What matrix has [23] 3 as its coordinate vector? as an ordered basis.