Consider the ordered bases B = (space V of upper triangular 2 x 2 matrices.a. Find the transition matrix from C to B.T² =[M] B =2b. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is [M]c =-G2c. Find M.) and C=M =[83][2²3][32]) for the vector

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Answered: T² = space V of upper triangular 2 x 2…

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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{a, ,a2.a3} be bases for a vector space V, and suppose a, = 4b1 - b2, a2 = - b, + 6b2 + b3, az = b2 - 3b3. Let A = and B = a. Find the change-of-coordinates matrix from A to B. b. Find [x]B for x = 4a1 + 5a2 + a3. ... 4 - 1 a. P = - 1 1 BEA 1 - 3 b. [x]B (Simplify your answer.)
b. Let B = {T1, đ2, T3}, C = {71, 72, 73}, be two orthogonal bases for R$. Show that the change-of-coordinates matrix PB¬c is orthogonal.
7,,
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T² = space V of upper triangular 2 x 2 matrices. a. Find the transition matrix from C to B. [M]B = Consider the ordered bases B = ( & c. Find M. M = 2 an b. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is [M]c = - ) and C= [83][²3][32] 2 2 ) for the vector