Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Determine whether the vector v is in the span of a set S, where a) v = (2 -1 1 3) and s=(101 -1), (0 11 1)} in R4 b) v = - x³ +2x?-3x-3 and S={x°+ x? + x+1, x²+x+1, x+1} in P3

Determine whether the vector v is in the span of a set S, where a) v = (2 -1 1 3) and s=(101 -1), (0 11 1)} in R4 b) v = - x³ +2x?-3x-3 and S={x°+ x? + x+1, x²+x+1, x+1} in P3

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 21EQ
See similar textbooks
icon
Related questions
Question
Provide complete and clear solution for each question. Work Problem 1 Determine whether the vector v is in the span of a set S, where a) v = (2 -1 1 3) and S=((101 -1), (0 11 1)} in R4 b) v = - x³+2x2-3x-3 and S={x³+x?+x+1, x²+x+1, x+1} in P3 Work Problem 2 ): Consider the vectors from R3 a V3 = 4 a) Create the augmented matrix which correspond to the equation X,V,+X,V2+ X3V3 =0 b) By using the REF form of the matrix created in part a, determine the conditions on the scalars a, b ER so that the set S = {v,, V2.V3} is linearly dependent %3D Work Problem 3 ( ): Given the vectors in R3 . (11 c), (-10 1), (-2 1 2). a) Find the value of c, for which given vectors are linearly dependent b) Express the first one as a linear combination of two others.
Transcribed Image Text:Provide complete and clear solution for each question. Work Problem 1 Determine whether the vector v is in the span of a set S, where a) v = (2 -1 1 3) and S=((101 -1), (0 11 1)} in R4 b) v = - x³+2x2-3x-3 and S={x³+x?+x+1, x²+x+1, x+1} in P3 Work Problem 2 ): Consider the vectors from R3 a V3 = 4 a) Create the augmented matrix which correspond to the equation X,V,+X,V2+ X3V3 =0 b) By using the REF form of the matrix created in part a, determine the conditions on the scalars a, b ER so that the set S = {v,, V2.V3} is linearly dependent %3D Work Problem 3 ( ): Given the vectors in R3 . (11 c), (-10 1), (-2 1 2). a) Find the value of c, for which given vectors are linearly dependent b) Express the first one as a linear combination of two others.
Expert Solution
steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS