Justify your explanation clearly. Let TA : R" –→ R" be multiplication by an invertible matrix A. Suppose that B = {b¡, b2, ..., b,} is a basisfor R".Prove that T(B) = {T(b¡), T(b2), ... ,T(b,)} is also a basis for R".

The given linear transformation is TA:ℝn→ℝn by multiplication by invertible matrix A. That is: Tx=Ax…

Answered: Let TA : R" → R" be multiplication by…

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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Let TA : R" → R" be multiplication by an invertible matrix A. Suppose that B = for R". {b1, b2, ... , b,} is a basis Prove that T(B) = {T(b1), T(b2), ... ,T(b,)} is also a basis for R".