Let FR" → R" and be a linear transformation. Suppose the matrix representation of F with respect to the standard basis B := {₁,..., en} CR" is an n x n matrix A. Show that the following linear transformation F(³): R¹ →R", F3³)(v):= F(F(F(v))) has matrix representation with respect to the basis B given by the matrix A³. Justify your answer.

Let FR" → R" and be a linear transformation. Suppose the matrix representation of F with respect to the standard basis B := {₁,..., en} CR" is an n x n matrix A. Show that the following linear transformation F(³): R¹ →R", F3³)(v):= F(F(F(v))) has matrix representation with respect to the basis B given by the matrix A³. Justify your answer.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.2: The Kernewl And Range Of A Linear Transformation

Problem 59E: Let T:R3R3 be the linear transformation that projects u onto v=(2,1,1). (a) Find the rank and...

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