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1: = 2 -1 1 2 4 1-3 5-2 1 3 4-2 5 -2 1 3 3 -1 4 -1 2-4-2 7 2 - 4 P = 90 3 4 1 0-45 0 0 0 18 90 90 RREF(A) 0 16 0 -20 0 19 0 45 -45 45 -45 00 90 45 10 10 -5 - 45 0 0 0 45 0 0 0 0 0 45 0 0 00 -4 41 47 50 40 -25 61 16 0 0 00 (a) Describe the associated transformation T: R6 → R5 (b) Give a basis of the null space of A. (c) Give a basis for the column space of A. (d) Represent one column as a linear combination of the other columns. (e) Give a basis for the Range of T. (f) Give a basis for the Eigenspace (Espace(0)) of the Eigenvalue 0. (g) Let v = [1,2,3,4,5]. Write v as a linear combination of the of the basis vectors in R6 = Espace (0) + Espace(0)+ 8 0 0

1: = 2 -1 1 2 4 1-3 5-2 1 3 4-2 5 -2 1 3 3 -1 4 -1 2-4-2 7 2 - 4 P = 90 3 4 1 0-45 0 0 0 18 90 90 RREF(A) 0 16 0 -20 0 19 0 45 -45 45 -45 00 90 45 10 10 -5 - 45 0 0 0 45 0 0 0 0 0 45 0 0 00 -4 41 47 50 40 -25 61 16 0 0 00 (a) Describe the associated transformation T: R6 → R5 (b) Give a basis of the null space of A. (c) Give a basis for the column space of A. (d) Represent one column as a linear combination of the other columns. (e) Give a basis for the Range of T. (f) Give a basis for the Eigenspace (Espace(0)) of the Eigenvalue 0. (g) Let v = [1,2,3,4,5]. Write v as a linear combination of the of the basis vectors in R6 = Espace (0) + Espace(0)+ 8 0 0

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.1: Introduction To Linear Transformations
Problem 39E: For the linear transformation from Exercise 33, find a T(1,1), b the preimage of (1,1), and c the...
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1: = 2 -1 1 2 4 1-3 5-2 1 3 4-2 5 -2 4 3 -1 - -1 1 3 2-4-2 24 7 4 2 P = 90 4 3 1 90 RREF(A) 0-45 0 16 0 0 0-20 0 18 0 19 90 0 45 45 00 90 45 10 10 -5 -45 -45 - 45 0 0 0 45 0 0 0 0 0 45 0 0 00 -4 41 47 50 40 -25 61 16 0 0 00 (a) Describe the associated transformation T: R6 → R5 (b) Give a basis of the null space of A. (c) Give a basis for the column space of A. (d) Represent one column as a linear combination of the other columns. (e) Give a basis for the Range of T. (f) Give a basis for the Eigenspace (Espace(0)) of the Eigenvalue 0. (g) Let v = [1,2,3,4,5]. Write v as a linear combination of the of the basis vectors in R6 = Espace (0) + Espace(0)+ 8 0 0
Transcribed Image Text:1: = 2 -1 1 2 4 1-3 5-2 1 3 4-2 5 -2 4 3 -1 - -1 1 3 2-4-2 24 7 4 2 P = 90 4 3 1 90 RREF(A) 0-45 0 16 0 0 0-20 0 18 0 19 90 0 45 45 00 90 45 10 10 -5 -45 -45 - 45 0 0 0 45 0 0 0 0 0 45 0 0 00 -4 41 47 50 40 -25 61 16 0 0 00 (a) Describe the associated transformation T: R6 → R5 (b) Give a basis of the null space of A. (c) Give a basis for the column space of A. (d) Represent one column as a linear combination of the other columns. (e) Give a basis for the Range of T. (f) Give a basis for the Eigenspace (Espace(0)) of the Eigenvalue 0. (g) Let v = [1,2,3,4,5]. Write v as a linear combination of the of the basis vectors in R6 = Espace (0) + Espace(0)+ 8 0 0
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