Question

1 -1 -b 1 The inverse of matrix A is (see explanation in Sec. 5.6) and d lo+Go A-1 1 1-blb 1 Thus the solution of the model isx A d, or CISE 4.6 1.Given A-B1--B -t].and c-l 1 0 9 ].find A, e-arnd C -1 3 , find A, 8', and C 2. Use the matrices given in Prob. 1 to verify that 3. Generalize the result (4.11) to the case of a product of three matrices by proving that, 4. Given the following four matrices, test whether any one of them is the inverse of (o) (A + By AB' (b) (ACY CA for any conformable matrices A, 8, and C, the equation (ABC), another: C'BA' holds. 1 12 S. Ceneraize the resut (4 14) by proving that, for any conformable nonsingular macices 6. Let A-I-X(xx)-1x le nonsingular matrices A, B, and C, the equation (ABC)C-18-1-1 holds. (o) Must A be square? Must (x'x) be square? Must X be square? (b) Show that matrix A is idempotent. Note: If X'and X are not square, it is inappro- priate to apply (4.14)] 4.7 Finite Markov Chains A common application of matrix algebra is found in what is known as Markov processes or

Answer 1