Let S =i.ii.tSpec)-SShow that S is a subspace of R4Find two vectors that span SAre the two vectors from (ii) linearly independent?Is S = R¹?iii.iv.[2ss, te R

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Answered: Let S = i. ii. iv. [2s- - S s,te R t…

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...

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Similar questions

Let S={v1,v2,v3} be a set of linearly independent vectors in R3. Find a linear transformation T from R3 into R3 such that the set {T(v1),T(v2),T(v3)} is linearly dependent.
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.
Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that among all the scalar multiples cv of the vector v, the projection of u onto v is the closest to u that is, show that d(u,projvu) is a minimum.
Consider the vector v=(1,3,0,4). Find u such that a u has the same direction as v and one-half of its length. b u has the direction opposite that of v and twice its length.

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Let S = i. ii. iv. [2s- - S s,te R t Inter} -S Show that S is a subspace of R4 Find two vectors that span S Are the two vectors from (ii) linearly independent? Is S = R¹?