Let V = Poly2 be the vector space of polynomials of degree 2 or less and let W = Poly, be the vector space of polynomials of degree 2 or less. Let B be the following basis for V and let B' be the following basis for W. B = ((1+1æ + 0x²), (0 + 0x + (–1)x²), (0+lx+0x²)) B' = ((-1+2x + (-1)x²), (0+ læ + 0x²), (1+ (–2)x + 0x²)) Suppose that T :V → W is a linear map and that the matrix associated to T with respect to the bases Band B' is: -2 -1 -2 [T]g'+B = -4 -1 -3 -1 -1 Find the value of T ((0+1æ + (-–2)x²)).
Let V = Poly2 be the vector space of polynomials of degree 2 or less and let W = Poly, be the vector space of polynomials of degree 2 or less. Let B be the following basis for V and let B' be the following basis for W. B = ((1+1æ + 0x²), (0 + 0x + (–1)x²), (0+lx+0x²)) B' = ((-1+2x + (-1)x²), (0+ læ + 0x²), (1+ (–2)x + 0x²)) Suppose that T :V → W is a linear map and that the matrix associated to T with respect to the bases Band B' is: -2 -1 -2 [T]g'+B = -4 -1 -3 -1 -1 Find the value of T ((0+1æ + (-–2)x²)).
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.1: Orthogonality In Rn
Problem 34EQ
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