Math 416-D13, Abstract Linear Algebra, Spring 2017 Homework 6, Due Friday, March 10, 2017 Read [FIS] Sections 4.1-4.2 Problems 1. Suppose T : V W is a linear transformation between finite-dimensional vector spaces and = {v1 , . . . , vn } is a basis for V . Prove that T is an isomorphism if and only if = {T (v1 ), . . . , T (vn )} is a basis for W . 2. Section 2.5 Problem 1 in [FIS]. No justification is necessary. 3. Section 2.5 Problem 2 in [FIS]. 4. Section 2.5 Problem 3(b), (d) in [FIS]. 5. Section 2.5 Problem 6(b), (d) in [FIS]. 6. Compute the determinants of the following matrices: \u0012 \u0013 \u0012 \u0013 \u0012 \u0013 1 3 3 2 3 4 (a) , (b) (c) 2 9 5 1 2 3 7. Section 4.1 Problems 5, 6 in [FIS]. 8. Section 4.2 Problem 6 in [FIS]. 9. Section 4.2 Problem 12 in [FIS]. 10. Section 4.2 Problem 21 in [FIS]. \f\f\f