Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
3. Consider the set S {1x², -x + 2x2,1 + 2x - x²} in P2 (R). Attempting to find a linear dependence is equivalent to finding a non-trivial solution (a, b, c) to a system of linear equations = a(1-x²) + b(-x+ 2x²) + c(1 + 2x - x²) = =0⇒>> (0 0 0) 11 a+c=0 -b+2c=0 -a +2b-c=0 C:

3. Consider the set S {1x², -x + 2x2,1 + 2x - x²} in P2 (R). Attempting to find a linear dependence is equivalent to finding a non-trivial solution (a, b, c) to a system of linear equations = a(1-x²) + b(-x+ 2x²) + c(1 + 2x - x²) = =0⇒>> (0 0 0) 11 a+c=0 -b+2c=0 -a +2b-c=0 C:

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Systems Of Linear Equations
Section1.1: Introduction To Systems Of Linear Equations
Problem 90E: Consider the system of linear equations in x and y. ax+by=ecx+dy=f Under what conditions will the...
See similar textbooks
icon
Related questions
Question
100%

Please do it by using matrix. Thank you!

3. Consider the set S {1 − x², −x + 2x²,1 + 2x − x²} in P₂ (R). Attempting to find a linear dependence is equivalent to finding a non-trivial solution (a, b, c) to a system of linear equations = a(1-x²)+b(-x+ 2x²) + c(1 + 2x - x²) = 0 ⇒ a+c=0 -b+2c=0 -a +2b-c=0 Since the only solution is trivial (a, b, c) = (0,0,0), the set S is linearly independent.
Transcribed Image Text:3. Consider the set S {1 − x², −x + 2x²,1 + 2x − x²} in P₂ (R). Attempting to find a linear dependence is equivalent to finding a non-trivial solution (a, b, c) to a system of linear equations = a(1-x²)+b(-x+ 2x²) + c(1 + 2x - x²) = 0 ⇒ a+c=0 -b+2c=0 -a +2b-c=0 Since the only solution is trivial (a, b, c) = (0,0,0), the set S is linearly independent.
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

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
Algebra for College Students
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
SEE MORE TEXTBOOKS