Homework Help is Here – Start Your Trial Now!
Math
Algebra
8. Decide which of the following sets are linearly independent in R". Justify your answer in each case. (a) X₁ = {(1,0), (0, 1)} ℃ R² (b) X₂ = {(1,0), (2,0)} CR² (c) X3 = {(-1,0), (0,0)} ℃ R²

8. Decide which of the following sets are linearly independent in R". Justify your answer in each case. (a) X₁ = {(1,0), (0, 1)} ℃ R² (b) X₂ = {(1,0), (2,0)} CR² (c) X3 = {(-1,0), (0,0)} ℃ R²

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 78E: Let S={v1,v2,v3} be a set of linearly independent vectors in R3. Find a linear transformation T from...
See similar textbooks
icon
Related questions
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)} ℃ R² (b) X₂ = {(1,0), (2,0)} ℃ R² (c) X3 = {(-1,0), (0, 0)} CR² 2 (d) X₁ = {(1,0), (0, 1), (1, 1)} ℃ R² C (e) X5 = {(1,0,0), (0, 1, 0), (1, 1, 1)} ℃ R³ (f) X6 = {(1,0,0), (0, 1, 0), (1, 1, 1), (−1, 0, 1)} ℃ R³ (g) X7 = {(0, 0, 0), (0, 1, 0), (1, 1, 1), (−1, 0, 1)} ℃ R³ (h) Xs = {(0, 1, 0), (1, 1, 1)} ℃ R³ 8 (i) X9 = {(4,3,0,0), (0, 0, 1, 1), (0, 0, 0, 1), (1, 0, 0, 1), (0, 1, 0, 1)} ℃ R4 (j) X10 = {(1, 2, 0, 0), (0, 2, 3, 0), (0, 0, −1, 1)} ℃ Rª
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)} ℃ R² (b) X₂ = {(1,0), (2,0)} ℃ R² (c) X3 = {(-1,0), (0, 0)} CR² 2 (d) X₁ = {(1,0), (0, 1), (1, 1)} ℃ R² C (e) X5 = {(1,0,0), (0, 1, 0), (1, 1, 1)} ℃ R³ (f) X6 = {(1,0,0), (0, 1, 0), (1, 1, 1), (−1, 0, 1)} ℃ R³ (g) X7 = {(0, 0, 0), (0, 1, 0), (1, 1, 1), (−1, 0, 1)} ℃ R³ (h) Xs = {(0, 1, 0), (1, 1, 1)} ℃ R³ 8 (i) X9 = {(4,3,0,0), (0, 0, 1, 1), (0, 0, 0, 1), (1, 0, 0, 1), (0, 1, 0, 1)} ℃ R4 (j) X10 = {(1, 2, 0, 0), (0, 2, 3, 0), (0, 0, −1, 1)} ℃ Rª
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS