4.Consider the subspace U of R4[X] given byU = {a+bx+cX² +dX³ + eX¹: a +2c= 0 and b-3c=0}Find a basis for U and determine dim(U). Make sure to prove that your proposed basisis indeed a basis for U.

The given subspace,.The aim is to find the basis of the subspace and the dimension of the subspace.

Answered: Consider the subspace U of R₁[X] given…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 44E: Prove that in a given vector space V, the additive inverse of a vector is unique.

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Consider the subspace U of R₁[X] given by U = {a+bx+cX² +dX³ +eX4:a+2c= 0 and b-3c=0} Find a basis for U and determine dim(U). Make sure to prove that your proposed basis is indeed a basis for U.