Let v1 = (4,6,7)T,v2 =(0,1,1)T, and v3 = (0,1,2)T ,and let u1 =(1,1,1), u2 = (1,2,2)T, and u3 = (2,3,4)T. Find the transition matrix from {v1,v2,v3}to{u1,u2,u3}. If x= 2v1+3v2−4v3, determine the coordinates of x with respect to {u1,u2,u3}.

Let v1 = (4,6,7)T,v2 =(0,1,1)T, and v3 = (0,1,2)T ,and let u1 =(1,1,1), u2 = (1,2,2)T, and u3 = (2,3,4)T. Find the transition matrix from {v1,v2,v3}to{u1,u2,u3}. If x= 2v1+3v2−4v3, determine the coordinates of x with respect to {u1,u2,u3}.

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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Question

Let v₁ = (4,6,7)^T,v₂=(0,1,1)^T, and v₃ = (0,1,2)^T,and let u₁ =(1,1,1),

u₂ = (1,2,2)^T, and u₃ = (2,3,4)^T.

Find the transition matrix from {v₁,v₂,v₃}to{u₁,u₂,u₃}.
If x= 2v₁+3v₂−4v₃, determine the coordinates of x with respect to {u₁,u₂,u₃}.

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