(a) Solve each of the following systems using the Cramer's Rule only. i. ii. (b) If...

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(a) Solve each of the following systems using the Cramer's Rule only. i. ii. (b) If A = 1 2 H100 3 1 2 and show that AB ‡ BA. I -2 3 3 -1 and B = 321 2 -18518 718 + LIU LUBU COIN - x 2 I 12 X + + 6 y 2 - y 3 + 1 - + 1 6 2 9 + = 14 IN NICT 10 = 1 2 <= 24 11 25 = -26 + = 13 2 (c) Let T: R→ R be a linear transformation such that T(1,0,0) = (2,-1,4) T(0, 1,0)= (1,5,-2) T(0,0,1)= (0, 3, 1). (8 marks) 1 0 2 0 1 2 obtain the product AB and BA 120 (8 marks) 1 2 0 4 0 0 7 001 200-2 0 0 0 0 1 0 4 00000 1 3 000000 k (7 marks) Find T(2,3,-2). (d) Find the transformation that will transform 10r²+2y² +52² +6yz-10zx-4.xy into a sum of square and find its reduced form. (5 marks) (10 marks) (e) Find all solutions of the system whose augmented matrix has been reduced to (8 marks) (a) Solve each of the following systems using the Cramer's Rule only. i. ii. (b) If A = 1 2 H100 3 1 2 and show that AB ‡ BA. I -2 3 3 -1 and B = 321 2 -18518 718 + LIU LUBU COIN - x 2 I 12 X + + 6 y 2 - y 3 + 1 - + 1 6 2 9 + = 14 IN NICT 10 = 1 2 <= 24 11 25 = -26 + = 13 2 (c) Let T: R→ R be a linear transformation such that T(1,0,0) = (2,-1,4) T(0, 1,0)= (1,5,-2) T(0,0,1)= (0, 3, 1). (8 marks) 1 0 2 0 1 2 obtain the product AB and BA 120 (8 marks) 1 2 0 4 0 0 7 001 200-2 0 0 0 0 1 0 4 00000 1 3 000000 k (7 marks) Find T(2,3,-2). (d) Find the transformation that will transform 10r²+2y² +52² +6yz-10zx-4.xy into a sum of square and find its reduced form. (5 marks) (10 marks) (e) Find all solutions of the system whose augmented matrix has been reduced to (8 marks)