Tugas Kelompok ke-1 (Minggu 3 / Sesi 4) 2 1 1 0 3 1. Given two matrices A and B 4 3 . Compute AB , BA , A BT 2 5 0 5 6 and AT B . 2. Given these matrices: 1 4 0 8 A , 1 9 8 9 2 1 1 2 0 0 B 1 0 , C and D 3 1 3 0 1 0 0 6 4 0 . 0 1 5 0 Compute BCA DT . 3. Given two matrices AB T 1 1 0 1 1 1 A 1 0 1 and B 1 1 1. Verify the property 0 1 1 1 1 1 BT AT . 4. Find the solution of these systems of linear equations using elimination methods as in high school: a. x 2y 3 4x 5 y 6 . x 3 y 4z 9 b. 3 x 2 y 2 z 20 . 5 x y 3 z 5 x y z w 1 c. x 2 y 3 z 4w 5 x 4 y 9 z 16 w 25 . x 8 y 27 z 64 w 125 MATH6078 - Linier Algebra 5. Given a system of linear equations: 3 x 2 y z 10 2 x y 5 z 19 , x y a z 6a 3 2 where a is a constant. a. If a 2 , does the system consistent? If yes, find the solution. If no, explain the reason. b. If a 0 , does the system consistent? If yes, find the solution. If no, explain the reason. c. If a 2 , does the system consistent? If yes, find the solution. If no, explain the reason. K0292 - Linier Algebra