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Supplementary Problems In Problems 1.19 through 1.32 let A = [1 2; 3 -4] B = [0 2; 1 2] C = [3 5 0; -2 -3 1; 1 2 1] D = [2 2 1; 4 4 2; 6 6 3] E = [1; 2; 3] F = [1, 2, 3] 1.19 Find (a) A + B; (b) 3A; (c) 2A - 3B; (d) C - D; and (e) A + F. 1.20 Designate the columns of A as A_1 and A_2, and the columns of C as C_1, C_2, and C_3, from left to right. Then calculate (a) A_1 · A_2; (b) C_1 · C_2; and (c) C_1 · C_3. 1.21 Find (a) AB; (b) BA; (c) (AB)^T; (d) B^T A^T; and (e) A^T B^T. 1.22 Find (a) CD and (b) DC. 1.23 Find A(A + B). 1.24 Find (a) CE and (b) EC. 1.25 Find (a) CF and (b) FC. 1.26 Find (a) EF and (b) FE. 1.27 Transform A to row-echelon form. 1.28 Transform B to row-echelon form. 1.29 Transform C to row-echelon form. 1.30 Transform D to row-echelon form. 1.31 Transform E to row-echelon form. 1.32 Find the rank of (a) A; (b) B; (c) C; (d) D; and (e) E. 1.33 Find two matrices, neither of which is a zero matrix, whose product is a zero matrix. 1.34 The price schedule for a New York to Miami flight is given by the vector P = [240, 180, 89], where the elements denote the costs of first class, business class, and tourist class tickets, respectively. The number of tickets of each class purchased for a particular flight is given by the vector N = [8, 21, 115]. What is the significance of P · N? 1.35 The inventory of computers at each outlet of a three-store chain is given by the matrix N = [9 12; 15 4; 7 0] where the rows pertain to the different stores and the columns denote the number of brand X and brand Y computers, respectively, in each store. The wholesale costs of these computers are given by the vector D = [700, 1200]^T. Calculate ND and state its significance.

          Supplementary Problems
In Problems 1.19 through 1.32 let
A = [1 2; 3 -4] B = [0 2; 1 2] C = [3 5 0; -2 -3 1; 1 2 1] D = [2 2 1; 4 4 2; 6 6 3] E = [1; 2; 3] F = [1, 2, 3]

1.19 Find (a) A + B; (b) 3A; (c) 2A - 3B; (d) C - D; and (e) A + F.

1.20 Designate the columns of A as A_1 and A_2, and the columns of C as C_1, C_2, and C_3, from left to right. Then calculate (a) A_1 · A_2; (b) C_1 · C_2; and (c) C_1 · C_3.

1.21 Find (a) AB; (b) BA; (c) (AB)^T; (d) B^T A^T; and (e) A^T B^T.

1.22 Find (a) CD and (b) DC.

1.23 Find A(A + B).

1.24 Find (a) CE and (b) EC.

1.25 Find (a) CF and (b) FC.

1.26 Find (a) EF and (b) FE.

1.27 Transform A to row-echelon form.

1.28 Transform B to row-echelon form.

1.29 Transform C to row-echelon form.

1.30 Transform D to row-echelon form.

1.31 Transform E to row-echelon form.

1.32 Find the rank of (a) A; (b) B; (c) C; (d) D; and (e) E.

1.33 Find two matrices, neither of which is a zero matrix, whose product is a zero matrix.

1.34 The price schedule for a New York to Miami flight is given by the vector P = [240, 180, 89], where the elements denote the costs of first class, business class, and tourist class tickets, respectively. The number of tickets of each class purchased for a particular flight is given by the vector N = [8, 21, 115]. What is the significance of P · N?

1.35 The inventory of computers at each outlet of a three-store chain is given by the matrix
N = [9 12; 15 4; 7 0]
where the rows pertain to the different stores and the columns denote the number of brand X and brand Y computers, respectively, in each store. The wholesale costs of these computers are given by the vector D = [700, 1200]^T. Calculate ND and state its significance.

Added by Daniela R.

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