a) Consider the linear system

3x+y=k\ k^(2)x+3y=-9

\ For which values of

k

does the linear system has\ i. A unique solution.\ ii- Infinitely many solutions\ iir. No solution.\ b) Consider the linear system in part a. solve it at

k=2

.\ c) Consider the linear system

Ax=B

in part a. For which values of

k

does the\ determenet of the coefficient matrix

A

equal -7 .\ Q-4[6+4*5 marks]:\ a) Let

A=[[0,2,3],[1,1,-1],[-1,1,-5]]

.\ i. Is

A

invertable. Justify your answer.\ ii- Find

|2A^(2)A^(-1)|

, and

|3A^(TT)|

.\ b) Let

A=[[1,0,-1],[2,1,3]]

and

B=[[1,2],[-1,0],[-2,1]]

. Find a matrix

C

, such that

C=A-3B^(r)

.

Q 3[8+4+3 marks]: a) Consider the linear system {3x+y=kk2x+3y=9 For which values of k does the linear system has i. A unique solution. it. Infinitely many solutions iir- No solution. b) Consider the linear system in part a. solve it at k=2. c) Consider the linear system AX=B in part a. For which values of k does the determenet of the coefificient matrix A equal -7 . Q-4[6+4+5 marks]: a) LetA=011211315, i- Is A invertable. Justify your answer. ii- Find 2A2A1, and 3A. b) Let A=[120113] and B=112201. Find a matrix C, such that C=A3Br. Q 3[8+4+3 marks]: a) Consider the linear system {3x+y=kk2x+3y=9 For which values of k does the linear system has i. A unique solution. it. Infinitely many solutions iir- No solution. b) Consider the linear system in part a. solve it at k=2. c) Consider the linear system AX=B in part a. For which values of k does the determenet of the coefificient matrix A equal -7 . Q-4[6+4+5 marks]: a) LetA=011211315, i- Is A invertable. Justify your answer. ii- Find 2A2A1, and 3A. b) Let A=[120113] and B=112201. Find a matrix C, such that C=A3Br