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Name(s): Score: Math 148 Lab Assignment 4: §9.1-9.2 Directions: You may work in groups of 2–3 to complete this assignment. Answer each question completely. Show all work to receive full credit, and circle your final answer. 1. Solve the linear system 5x − y + 2z = 6 x + 2y − z = −1 3x + 2y − 2z = 1 by finding the augmented matrix and performing Gaussian elimination. (Note: You must indicate which operation(s) you perform in each step of your solution.) 1 2. Determine whether the linear system x − 2y + z = 3 2x − 3y + z = 8 is overdetermined or underdetermined and solve the system by finding the augmented matrix and performing Gaussian elimination. (Note: You must indicate which operation(s) you perform in each step of your solution.) 2 3. Let 3 1 4 A = −2 0 1 1 2 2 and Compute the following: (a) AB (b) BA (c) (2A)T − (3B)T 3 1 0 2 B = −3 1 1 2 −4 1 4. Let 2 1 A = 6 3 −2 4 and 2 4 B= 1 6 Verify that (AB)T = B T AT . 5. Determine whether each matrix is singular or nonsingular. Find its inverse, if it exists. 4 6 (a) A = 6 9 3 1 (b) B = 4 2 4