Let T: P₂ → R² be the linear transformation. Given that M = (1,x+x²,2-3x2) and N = {(₁).(2)} are bases for P2 and R² respectively. a) Let T(a + bx + cx²) = (+b). i. Find the standard matrix, A for T such that T(v) = Av for v € P₂. ii. Find [T]NM, the matrix of T with respect to the bases M and N. b) If [v]M2, find T(v) using matrix [T]NM obtained in (a). -11-₁

Let T: P₂ → R² be the linear transformation. Given that M = (1,x+x²,2-3x2) and N = {(₁).(2)} are bases for P2 and R² respectively. a) Let T(a + bx + cx²) = (+b). i. Find the standard matrix, A for T such that T(v) = Av for v € P₂. ii. Find [T]NM, the matrix of T with respect to the bases M and N. b) If [v]M2, find T(v) using matrix [T]NM obtained in (a). -11-₁

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.6: The Matrix Of A Linear Transformation

Problem 17EQ

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