2Let R4 be the vector space over R with standard addition and scalarmultiplication. Let X = {(x, y, z, w) = R¹ : x-2y3z - 4w=0}. Show that X is a subspaceof R4. Find a basis for X and dim.X.

Answered: 2 Let R¹ be the vector space over R…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.2: Inner Product Spaces

Problem 101E: Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that...

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2 Let R¹ be the vector space over R with standard addition and scalar multiplication. Let X = {(x, y, z, w) = R¹ : x - 2y - 32 - 4w = 0}. Show that X is a subspace of R4. Find a basis for X and dimX.