Consider the vector space V of polynomials p(x) E P*(x) d? dr2 P(1) = 0 } . The dimension of V is four. satisfying Describe your isomorphism Iso by giving the elements of V satisfying the following: Iso(a1,0 + a1,1 x + aj,2 x² +a1,3 x³ + a\,4 xrt) = [1,0,0, 0] where Iso(a20 + a21 x + a22 x² +a23 x³ + az4 x* ) = [0, 1,0, 0] where Iso(a30 + a3,1 x + a3,2 x² + a3,3 x³ + a,a x* ) = [0, 0, 1, 0] where Iso(a4,0 + a4,1 x + a4,2 x² + a4,3 x³ + a44 x* ) = [0, 0, 0, 1] where Iso(as,0 + as,1 x + as,2 x² +as,3 x³ + as,4 x* ) = [-1,2, –3, –1] where

Consider the vector space V of polynomials p(x) E P(x) d? dr2 P(1) = 0 } . The dimension of V is four. satisfying Describe your isomorphism Iso by giving the elements of V satisfying the following: Iso(a1,0 + a1,1 x + aj,2 x² +a1,3 x³ + a\,4 xrt) = [1,0,0, 0] where Iso(a20 + a21 x + a22 x² +a23 x³ + az4 x ) = [0, 1,0, 0] where Iso(a30 + a3,1 x + a3,2 x² + a3,3 x³ + a,a x* ) = [0, 0, 1, 0] where Iso(a4,0 + a4,1 x + a4,2 x² + a4,3 x³ + a44 x* ) = [0, 0, 0, 1] where Iso(as,0 + as,1 x + as,2 x² +as,3 x³ + as,4 x* ) = [-1,2, –3, –1] where

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 46E: CAPSTONE (a) Determine the conditions under which a set maybe classified as a vector space. (b) Give...

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