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= 2 1 1-3 5-2 4-2 5 -2 1 3 3-1 -4-2 3 2 4 24 134 1 2 -1 2 7 4 P || 90 RREF(A) 0 = 0-45 0 16 0 0 0 -20 0 18 0 19 90 90 0 45 -45 0 90 45 -45 45 10 10 -5 (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. 45 00 0 45 0 0 0 45 0 0 0 0 0 0 -4 41 47 50 40 -25 61 16 0 0 0 0 8 0 0

= 2 1 1-3 5-2 4-2 5 -2 1 3 3-1 -4-2 3 2 4 24 134 1 2 -1 2 7 4 P || 90 RREF(A) 0 = 0-45 0 16 0 0 0 -20 0 18 0 19 90 90 0 45 -45 0 90 45 -45 45 10 10 -5 (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. 45 00 0 45 0 0 0 45 0 0 0 0 0 0 -4 41 47 50 40 -25 61 16 0 0 0 0 8 0 0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.1: Polynomial Functions Of Degree Greater Than
Problem 31E
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1: = 2 1-3 5-2 -1 1 2 4 3 - 4 -1 1 4-2 5 -2 1 3 -1 3 2-4-2 24 7 4 2 P = 90 4 90 3 1 0-45 0 16 0 0 0-20 0 18 0 19 90 0 45 45 0 RREF(A) 0 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 1-3 5-2 -1 1 2 4 3 - 4 -1 1 4-2 5 -2 1 3 -1 3 2-4-2 24 7 4 2 P = 90 4 90 3 1 0-45 0 16 0 0 0-20 0 18 0 19 90 0 45 45 0 RREF(A) 0 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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