1O 1. Determine the value of the unknown in the given matrix equalities (f4 '32)+(i', )=( 21) (i) (ii) 2. Solve for x in the given matrix equalities X 73 4 det 3 5 x : 45 1 2 71 3. Determine the inverse of A, and show that A'IA :1. 2 1 0 A: 2 71 l 3 72 4 4. Use the matrix method (together with elementary row transformations) to solve the lollowing: (5i (5) iny +32 : 2 X2yz : 4 74X775y+z : 10. 5. The lollowing were obtained by applying Kirchoff's laws to an electric circuit ZIA+15710 = 78 4A +15 +10 : 3 7214 +410 : 18. MAT151 1/101/0/2022 (a) Determine the electric current 13 using matrix inversion. (4) (b) Determine the electric current IA and to using Cramer's Rule. (4) 6. Consider the following system of constraints, associated with a linear programming problem: x+2y S 12 X+y : 10 X 2 0 Y 2 0- Maximize z : X+4y. (5) 7. A housing contractor has subdivided a farm into 100 building lots. She has designed two types of homes for these lots: Colonial and ranch style. A colonial requires R30000 of capital and produces a profit of R4000 when sold. A ranchstyle house requires R40000 of capital and provides an H8000 profit. Ifthe contractor has R3.6 million of capital on hand, how many houses of each type should she build lor maximum profit? Will any of the lots be left vacant? (5) [45]