1. L(at² + bt+c) = bt² + (a−b)t+(a + c) Let S = (1²,1,1) be an ordered basis for P₂. (Hint: we're using the same ordered basis for both the domain and range). a. Let L: P₂ P₂ be defined by b. Find the matrix representation for L with respect to the ordered basis S. Using your answer to part (a), answer: Is L invertible? Provide full justification.

1. L(at² + bt+c) = bt² + (a−b)t+(a + c) Let S = (1²,1,1) be an ordered basis for P₂. (Hint: we're using the same ordered basis for both the domain and range). a. Let L: P₂ P₂ be defined by b. Find the matrix representation for L with respect to the ordered basis S. Using your answer to part (a), answer: Is L invertible? Provide full justification.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 37EQ

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