Consider the vector space PA(R) = {ax + bæ³ + ca? + dx + e : a, b, c, d, e E R} of polynomials of degree at most 4. Please find three distinct polynomials fi, f2, f3 that spans a 2-dimensional subspace. To type your answer, please type in the matrix P such that (fi(x) f2(x) f3(x))=(1 x x² r3 a4 ) P

Elementary Linear Algebra (MindTap Course List)
8th Edition
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Author:Ron Larson
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Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 41CR: 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...
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Find matrix P according to the concept in linear algebra, the solution of P should be a 5x3 matrix

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Consider the vector space
PA(R) = {ax* + ba + cx? + dx + e : a, b, c, d, e E R}
of polynomials of degree at most 4. Please find three distinct polynomials f1, f2, f3 that spans a 2-dimensional subspace. To type
your answer, please type in the matrix P such that
( fi(x) f2(x) f3(x))=(1 x x? x3 x4) P
Hint:
Transcribed Image Text:Consider the vector space PA(R) = {ax* + ba + cx? + dx + e : a, b, c, d, e E R} of polynomials of degree at most 4. Please find three distinct polynomials f1, f2, f3 that spans a 2-dimensional subspace. To type your answer, please type in the matrix P such that ( fi(x) f2(x) f3(x))=(1 x x? x3 x4) P Hint:
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