Let B ={Q.[3]}that{[] []}. Suppose[83]A=4is the matrix representation of a linear operator T: R² → R² with respect to B.(a) Determine T(-5,5).(b) Find the transition matrix P from B' to B.(c) Using the matrix P, find the matrix representation of T with respect to B'.and B' =

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Answered: Let B B-{B·[3]} and B-{[4]-8} B'…

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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Show that w is in span(B). We want to solve B - (-)-~-] = W = -1 Thus C₁ = 048 2 + C₂ so set up the augmented matrix of the linear system and row-reduce to solve it: [w] B = 12 1 1 0 0 -1 and C₂ = 00 8 [3]. + Find the coordinate vector [w]B. 3 R₂-2R₁ -=1/R₂2 R₁ - R₂ R₂ + R₂ 1 1 0-2 0 -1 1 0 1 0 -1 1 0 0 1 0 0 so that
Consider B = 2 B' = i) Show that B and B' are bases for R³. [9] ii) Find the coordinate matrices of v = |2| relative to the bases B and B'. iii) Find the transition matrix PB¬B' - iv) Verify that [x(v)]p' = Pg¬p'[x(v)]g- %3D
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5. 3 (a) Let A To which point does A map the point (2, –5)? To which point does A map the point (1,0)? 1 (b) Let B = To which point does B map the point (11, 8)? To 3 which point does B map the point (3, 4)? (c) Find the matrix which maps the point (2, –5) to the point (19, 13) and the point (1,0) to (7,9).
C: Let T be the linear operator associated in the standard basis B of F2 with the matrix 2 - [44] - 1 Let B' be the basis ((2, -1), (2, 1)) M = b) Using eachof these three matrices find the dimension of the range of T (you must check that the dimension is the same with all the matrices)
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Let B B-{B·[3]} and B-{[4]-8} B' Suppose that [32] A = 4 is the matrix representation of a linear operator T: R² → R² with respect to B. (a) Determine T(-5,5). (b) Find the transition matrix P from B' to B. (c) Using the matrix P, find the matrix representation of T with respect to B'.