MA 16100 Final: Final Exam Spring 2016 Solutions

2.3 Matrix Products 85 1 0 1 0 1 2 2 3 0 1 0 1 3 4 4 5 16. 0 0 1 0 0 0 1 2 0 0 0 1 J 0 0 3 4 In the Exercises 17 through 26, find all matrices that com- mute with the given matrix A. 18. A -3 2 0 -21 20. A 19 A 2 0 21. A 22. A 2 0 01 24. A 23. A 2 6 0 0 3 T2 0 01 2 0 01 26. A 25. A 27. Prove the distributive laws for matrices: A (C D) AC AD

1. Evaluate (3x-2-7x6 + 2) dr 2 mar b. 2. Evaluate ma 2 3. Assume that f,f(x)dr=10 jf(x)dx=15 and 12 ma Find 3s(x)dr a. 75 b. 15 C.-15 d. 75 4. Evaluate [(tan(2x)) sec2 (2r)dx 12 ma b. (tan 2x)' +c d. 8(tan 2x)+e a. tan 2x)+

A. 32/3 B. 22/3 C. 29/6 D. 20/3 E. 17/3 A. 4/3 B. 1/3 C. 5/3 E. 2