9. (a) Evaluate the matrix product Ax, where -}] Hence show that the system of linear...

 

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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-b₁ 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 A¹ and B¹. (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')". 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-b₁ 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 A¹ and B¹. (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')".

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9a 9b Exercise 71 1 2 3 9 a A AX f where L A S 3 G... View the full answer