9. (a) Evaluate the matrix product Ax, where -}] Hence show that the system of linear equations 7x + 5y = 3 x + 3y = 2 A = 1 and x = can be written as Ax=b where b = (b) The system of equations 2x + 3y - 2z = 6 x-y + 2z=3 4x + 2y + 5z = 1 can be expressed in the form Ax = b. Write down the matrices A, x and b. Exercise 7.1* 1. Matrices A, B, C and D have orders 3 x 5,5 x 2,5 x 5 and 3 x 5, respectively. State whether it is possible to perform the following matrix operations. If it is possible, state the order of the resulting matrix. (d) BC (a) 7B (b) (A + C) (e) CBT (f) D'A 2. Two matrices A and B are given by a-1 b A=la+b3c-b b ^ - [2 ? A -[2] b] (c) A - 2D (g) AT + BT and B- If A = B, find the values of a, b, c and d. 3. Consider the matrices gh }] and Bij kl 1 3a 2c d + (a) Write down the matrices A and B. (b) Work out the matrix products AB and BTAT. (c) State the relationship between AB and BTAT, and use this result to simplify (A'B'C')".