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8. Decide which of the following sets are linearly independent in R. Justify your answer in each case. (a) X₁ = {(1,0), (0, 1)} CR² (b) X₂= {(1,0), (2,0)} CR² (c) X3 = {(-1,0), (0,0)} CR²

8. Decide which of the following sets are linearly independent in R. Justify your answer in each case. (a) X₁ = {(1,0), (0, 1)} CR² (b) X₂= {(1,0), (2,0)} CR² (c) X3 = {(-1,0), (0,0)} CR²

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 4CM: Use a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4,...
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Question
8. Decide which of the following sets are linearly independent in R. Justify your answer in each case. (a) X₁ = {(1,0), (0, 1)} CR² (b) X₂ = {(1,0), (2,0)} CR² (c) X3 = {(-1,0), (0,0)} CR² (d) X₁ = {(1,0), (0, 1), (1, 1)} CR² (e) X5 = {(1,0,0), (0, 1, 0), (1, 1, 1)} CR³ (f) X6 = {(1,0,0), (0, 1, 0), (1, 1, 1), (-1,0,1)} CR³ (g) X7 = {(0, 0, 0), (0, 1, 0), (1, 1, 1), (-1,0,1)} CR³ (h) Xs = {(0, 1, 0), (1,1,1)} CR³ (i) X9 = {(4,3,0,0), (0, 0, 1, 1), (0, 0, 0, 1), (1, 0, 0, 1), (0, 1, 0, 1)} CR¹ (j) X10 = {(1,2,0,0), (0, 2, 3,0), (0, 0, -1, 1)} CR¹
Transcribed Image Text:8. Decide which of the following sets are linearly independent in R. Justify your answer in each case. (a) X₁ = {(1,0), (0, 1)} CR² (b) X₂ = {(1,0), (2,0)} CR² (c) X3 = {(-1,0), (0,0)} CR² (d) X₁ = {(1,0), (0, 1), (1, 1)} CR² (e) X5 = {(1,0,0), (0, 1, 0), (1, 1, 1)} CR³ (f) X6 = {(1,0,0), (0, 1, 0), (1, 1, 1), (-1,0,1)} CR³ (g) X7 = {(0, 0, 0), (0, 1, 0), (1, 1, 1), (-1,0,1)} CR³ (h) Xs = {(0, 1, 0), (1,1,1)} CR³ (i) X9 = {(4,3,0,0), (0, 0, 1, 1), (0, 0, 0, 1), (1, 0, 0, 1), (0, 1, 0, 1)} CR¹ (j) X10 = {(1,2,0,0), (0, 2, 3,0), (0, 0, -1, 1)} CR¹
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