9. Find all values of k, if any, that satisfy the equation. [1 2 01 [2]...

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9. Find all values of k, if any, that satisfy the equation. [1 2 01 [2] [22 k] 2 0 3|2|=0 Lo 3 1 kl 10. Use determinants to decide whether the given matrix is invertible and hence find the inverse. 4 2 8 2 5 51 -1 0 1-4 (ii) A = -1 1 6 2 4 3] (i) A = -2 3 a b C --:1 h 11. Let A = d e f, assuming that det(A) = 3, find [a b (a) det(2A) (b) det(A-¹) (c) det (3A-¹) (d) det((2A)-¹) (e) det d Lg h 12. Solve by Cramer's rule, where it applies. 4x + 5y = 2 11x + y + 2z = 3 x + 5y +2z = 1 14. Consider the system C 742 x + 2y +z = 3 ay + 5z = 10 2x + 7y + az = b e f 13. Reduce the system of linear equations to echelon form using Gauss elimination. Hence find the solution. x + 2y3z = -1 -3x + y - 2z = -7 5x + 3y - 4z = 2 i (a) Find those values of a for the system has a unique solution. (b) Find those pairs of values(a,b) for which the system has more than one solution. 9. Find all values of k, if any, that satisfy the equation. [1 2 01 [2] [22 k] 2 0 3|2|=0 Lo 3 1 kl 10. Use determinants to decide whether the given matrix is invertible and hence find the inverse. 4 2 8 2 5 51 -1 0 1-4 (ii) A = -1 1 6 2 4 3] (i) A = -2 3 a b C --:1 h 11. Let A = d e f, assuming that det(A) = 3, find [a b (a) det(2A) (b) det(A-¹) (c) det (3A-¹) (d) det((2A)-¹) (e) det d Lg h 12. Solve by Cramer's rule, where it applies. 4x + 5y = 2 11x + y + 2z = 3 x + 5y +2z = 1 14. Consider the system C 742 x + 2y +z = 3 ay + 5z = 10 2x + 7y + az = b e f 13. Reduce the system of linear equations to echelon form using Gauss elimination. Hence find the solution. x + 2y3z = -1 -3x + y - 2z = -7 5x + 3y - 4z = 2 i (a) Find those values of a for the system has a unique solution. (b) Find those pairs of values(a,b) for which the system has more than one solution.