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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
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