Check whether the set S of all vectors in R¹ given by426-85= {(a + 2b₁a+1.a)/a,b €R}is a subspace of R'or not. Justify your answers.02226-8

Given: The set S of all vectors in R3 given by S=(a+2b, a+1, a)/a,b∈R.

Answered: Check whether the set S of all vectors…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 60CR: Find the projection of the vector v=[102]T onto the subspace S=span{[011],[011]}.

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Similar questions

Find the projection of the vector v=[102]T onto the subspace S=span{[011],[011]}.
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Repeat Exercise 41 for B={(1,2,2),(1,0,0)} and x=(3,4,4). Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.
Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector u=(1,1,1,1) in the form u=v+w, where v is in V and w is orthogonal to every vector in V.
Give an example showing that the union of two subspaces of a vector space V is not necessarily a subspace of V.
Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.

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Check whether the set S of all vectors in R¹ given by 126-85=((a+2b₁a+1,a)/a,b ≤ R} is a subspace of R³ or not. Justify your answers.