Let TR R3 be the linear transformation given by X1 x2 T I3 == x4 3x19x25x3-7x4 - 9x5 2x16x23x3 -4x4-6x5 5x3 + 10x4 x5 (a) Find the image of T and find a basis for ImT. (b) Find the kernel of T and a basis for kerT. (c) Find the rank and nullity of T. Is the dimension of the domain of T equal to the sum of the rank and the nullity that you found?

Let TR R3 be the linear transformation given by X1 x2 T I3 == x4 3x19x25x3-7x4 - 9x5 2x16x23x3 -4x4-6x5 5x3 + 10x4 x5 (a) Find the image of T and find a basis for ImT. (b) Find the kernel of T and a basis for kerT. (c) Find the rank and nullity of T. Is the dimension of the domain of T equal to the sum of the rank and the nullity that you found?

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 52E: Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.

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