Let B={v_1...v_n} be a basis for R^n and let E be a standard basis for R^n. Let T: R^n ->R^n be the change of basis transformation T({x}b ) ={x}E . Prove that T is a bijection. (T is a matrix transformation).

Let B={v_1...v_n} be a basis for R^n and let E be a standard basis for R^n. Let T: R^n ->R^n be the change of basis transformation T({x}b ) ={x}E . Prove that T is a bijection. (T is a matrix transformation).

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 B={v_1...v_n} be a basis for R^n and let E be a standard basis for R^n. Let T: R^n ->R^n be the change of basis transformation T({x}_b) ={x}_E . Prove that T is a bijection.

(T is a matrix transformation).

Expert Solution

Proof:

Further follows,

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