Problem 9. (6 points) Let A be a 2 x 2 matrix. Given the following descriptions, determine the following elementary matr

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Problem 9 6 Points Let A Be A 2 X 2 Matrix Given The Following Descriptions Determine The Following Elementary Matr 1 (139.66 KiB) Viewed 60 times

Problem 9. (6 points) Let A be a 2 x 2 matrix. Given the following descriptions, determine the following elementary matrices and their inverses. a. The elementary matrix E multiplies the first row of A by 1/3. E = Ei b. The elementary matrix E, multiplies the second row of A by-3. E2 E, c. The elementary matrix E3 switches the first and second rows of A. E = ES Note: You can earn partial credit on this problem. Problem 10. (3 points) 2 V 1. If A and B are invertible n x n matrices, then (AB) -1 = A-B-1 ? 2. If a square matrix A is row equivalent to the identity matrix, then A is invertible ? 3. For any matrix A, the matrix AT A is symmetric. Note: You can earn partial credit on this problem. Problem 11. (6 points) Let A be a 2 x 7, B be a 7 x 9 and C be a 9 x 2 matrix. Determine the size of the following matrices (if they do not exist, type N in both answer boxes): X AB: BC: ABC: BCT: X X Note: You can earn partial credit on this problem.