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...

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

Extracted 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(a + bx + cx²) = (a,a+ b,a + b+ c). Find the matrix representation T relative to the standard basis.

Jun 04, 2022

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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...

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