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2. Let P2(C) be a vector space of polynomials of degree less than or equal to 2 over R. (a) By using linear extension method, show that P2(C) is isomorphic to C³. (b) Let T : P2(C) → C³ be a transformation such that T(a + bx + cx²) = (a, a + b, a + b+ c). Find the matrix representation T relative to the standard basis.

2. Let P2(C) be a vector space of polynomials of degree less than or equal to 2 over R. (a) By using linear extension method, show that P2(C) is isomorphic to C³. (b) Let T : P2(C) → C³ be a transformation such that T(a + bx + cx²) = (a, a + b, a + b+ c). Find the matrix representation T relative to the standard basis.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 34E
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2. Let P2(C) be a vector space of polynomials of degree less than or equal to 2 over R. (a) By using linear extension method, show that P2(C) is isomorphic to C³. (b) Let T : P2(C) → C³ be a transformation such that T(а+ ba + сa*) — (а, а + b,а +b+с). Find the matrix representation T relative to the standard basis.
Transcribed Image Text:2. Let P2(C) be a vector space of polynomials of degree less than or equal to 2 over R. (a) By using linear extension method, show that P2(C) is isomorphic to C³. (b) Let T : P2(C) → C³ be a transformation such that T(а+ ba + сa*) — (а, а + b,а +b+с). Find the matrix representation T relative to the standard basis.
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