(a) A business makes toy planes and toy cars. The following table show the items needed...

   

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(a) A business makes toy planes and toy cars. The following table show the items needed in calculating the cost of manufacturing each toy. Labour Wood Paint (Hours) (Blocks) (Tins) Plane 6 4 3 Car 3 4 2 Given labour cost RM 8 per hour, wood costs RM 5 per block and paint cost RM 2 per tin. (i) (ii) Write a 23 matrix A that represent the items needed in (2 marks) calculating the cost of manufacturing each toy and a column matrix B that represent each item cost per unit. Find matrix C that represent cost of manufacturing each type of (2 marks) toy from A and B obtained in (4) (a) (i) above. In addition, D=(300 100). (iii) Evaluate DC. (iv) Explain what DC represents. (2 marks) (1 mark) (b) 3 -1 0 Given matrix P= 2 1 1 -3, and Q-05 10 find 3P-Q. -2 0 4 -2) 2 -3 0 (3 marks) 1 (c) Solve the following system using Cramer's Rule. 4a+3b=4 2a+2b-2c=0 5a+3b+c=-2 (8 marks) (d) 2 3 -1 Find A where A= 12 5 using adjoint of matrix. 3-1-8 (e) Consider the system of linear equations below. (6 marks) 2x+3y-z=1 x+2y+5x=4 3x-y-8z=-7 Solve by writing the above as AX = B where X is the column unknown (5 marks) matrix using the results of A' from part (4) (d) above. (f) Write an example for 33 upper triangle matrix. (1 mark) (Total: 30 marks) ---END OF QUESTION PAPER- --- (a) A business makes toy planes and toy cars. The following table show the items needed in calculating the cost of manufacturing each toy. Labour Wood Paint (Hours) (Blocks) (Tins) Plane 6 4 3 Car 3 4 2 Given labour cost RM 8 per hour, wood costs RM 5 per block and paint cost RM 2 per tin. (i) (ii) Write a 23 matrix A that represent the items needed in (2 marks) calculating the cost of manufacturing each toy and a column matrix B that represent each item cost per unit. Find matrix C that represent cost of manufacturing each type of (2 marks) toy from A and B obtained in (4) (a) (i) above. In addition, D=(300 100). (iii) Evaluate DC. (iv) Explain what DC represents. (2 marks) (1 mark) (b) 3 -1 0 Given matrix P= 2 1 1 -3, and Q-05 10 find 3P-Q. -2 0 4 -2) 2 -3 0 (3 marks) 1 (c) Solve the following system using Cramer's Rule. 4a+3b=4 2a+2b-2c=0 5a+3b+c=-2 (8 marks) (d) 2 3 -1 Find A where A= 12 5 using adjoint of matrix. 3-1-8 (e) Consider the system of linear equations below. (6 marks) 2x+3y-z=1 x+2y+5x=4 3x-y-8z=-7 Solve by writing the above as AX = B where X is the column unknown (5 marks) matrix using the results of A' from part (4) (d) above. (f) Write an example for 33 upper triangle matrix. (1 mark) (Total: 30 marks) ---END OF QUESTION PAPER- ---