Let W = {(a, b, c, d)| 5a – c = 0 } be a subspace of R*. Then a basis for W is{(5,1,0,0),(0,0,1,0),(0,0,0,1)}{(1,0,5,0),(0,0,0,1)}{(1,0,5,0)}O {(1,0,5,0),(0,1,0,0),(0,0,0,1)}

Given : W=(a,b,c,d) | 5a-c=0 be a subspace of R4. we have to find a basis for W.

Answered: O {(1,0,5,0),(0,1,0,0),(0,0,0,1)}

Math

Algebra

O {(1,0,5,0),(0,1,0,0),(0,0,0,1)}

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.CR: Review Exercises

Problem 25CR

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Question

Let W = {(a, b, c, d)| 5a – c = 0 } be a subspace of R*. Then a basis for W is
{(5,1,0,0),(0,0,1,0),(0,0,0,1)}
{(1,0,5,0),(0,0,0,1)}
{(1,0,5,0)}
O {(1,0,5,0),(0,1,0,0),(0,0,0,1)}

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