Math 416-D13, Abstract Linear Algebra, Spring 2017 Homework 5, Due Friday, March 3, 2017 Read [FIS] Sections 2.3-2.5 Problems 1. Section 2.3 Problem 1 in [FIS]. 2. Section 2.3 Problem 2 in [FIS]. 3. Section 2.3 Problem 3 in [FIS]. 4. Let = {1, x, x2 } be the standard ordered basis of P2 (R). Consider the linear transformation T (f (x)) = f 00 (x) + f 0 (x) + f (x). T : P2 (R) P2 (R), (a) Find [T ] . (b) Use Theorem 2.14 [FIS] to compute [T (2x2 x + 1)] . (c) Check your answer by computing T (2x2 x + 1) directly from its definition. 5. Section 2.4 Problem 1 in [FIS]. 6. Section 2.4 Problem 2(a),(b) in [FIS]. 7. Section 2.4 Problem 3 in [FIS]. 8. Section 2.4 Problem 4 in [FIS]. 9. Section 2.4 Problem 5 in [FIS]. 10. (a) Find the inverse A1 of 1 2 3 1 2 4 0 3 1 (b) Verify that your answer is correct using the definition of the inverse