(c) Find P-1 and A' (the matrix for T relative to B').p-1 =A' =(d) Find [T(V)]g' two ways.[T(V)]g = P-1[T(v)]g[T(V)]g = A'[V]g = Let B = {(0, 1, 1), (1, 0, 1), (1, 1, 0)} and B' ={(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for R3, and let31-1225A =11.22be the matrix for T: R3 → R3 relative to B.(a) Find the transition matrix P from B' to B.P =(b) Use the matrices P and A to find [v]g and [7(V)]g, where[V]g = [1 -1 oj".[V]B =[T(V)]B2.

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Answered: Let B = {(0, 1, 1), (1, 0, 1), (1, 1,…

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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1. Let u₁, U2, U3 } and { V₁, V2, V3 } be ordered bases for R³, where H and U₁ = 2 1 U₂ = 1 V1 = 1 -1 -2 U3 = -8-0-0 V2 = 1 V3 (a) Determine the transition matrix corresponding to a change of basis from the ordered basis {u₁, U2,, u3} to the ordered basis {V₁, V2, V3}. (b) Write vector z = 2u₁ - 3u₂ + u3 as Use this transition matrix to find the coordinates of with respect to {V₁, V2, V3}.

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