Let TR5 R³ be the linear transformation given by X1 x2 T x3 x4 X5 x1 + 2x2 x3 + 2x4x5 2x14x22x3 + 5x4 + x5 2x14x22x3 + 6x5 (a) Find the image of T and a basis for it. (b) Find the kernel of T and a basis for it. (c) Find the rank and nullity of T. Is the dimension of the domain of T equal to the sum of the rank and nullity that you found?
Let TR5 R³ be the linear transformation given by X1 x2 T x3 x4 X5 x1 + 2x2 x3 + 2x4x5 2x14x22x3 + 5x4 + x5 2x14x22x3 + 6x5 (a) Find the image of T and a basis for it. (b) Find the kernel of T and a basis for it. (c) Find the rank and nullity of T. Is the dimension of the domain of T equal to the sum of the rank and nullity that you found?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 2EQ: Let TA: 23 be the matrix transformation corresponding to A=[311124]. Find TA(u) and TA(v), where...
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