Problem 1. Let T : R → M2x2(R) be the linear transformation defined as -4a 7b + 7c T(a, b, c, d) %3D 7c+7b -4d (a) Find a basis for Ker(T) and determine nullity(T). (b) Determine whether T is injective and surjective. (c) Find the matrix of T relative to the bases B and B', that is [TB'.B Wwhere 1 0 0 0 0 0 1 0 -1 = [e1, e2, e3, e4] and B' = %3D -1 -1

Problem 1. Let T : R → M2x2(R) be the linear transformation defined as -4a 7b + 7c T(a, b, c, d) %3D 7c+7b -4d (a) Find a basis for Ker(T) and determine nullity(T). (b) Determine whether T is injective and surjective. (c) Find the matrix of T relative to the bases B and B', that is [TB'.B Wwhere 1 0 0 0 0 0 1 0 -1 = [e1, e2, e3, e4] and B' = %3D -1 -1

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.3: Matrices For Linear Transformations

Problem 43E: Let T:P2P3 be the linear transformation T(p)=xp. Find the matrix for T relative to the bases...

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