24 September 2014
1) Discuss for all values of k the system of equations
2x+3ky+(3k+4)z=0,
x+(k+4)y+(4k+2)z=0,
x+2(k+1)y+(3k+4)z=0.
2) Investigate for what values of α and µ the simultaneous equations
x+y+z=6,x+2y+3z=10,x+2y+αz=µ
have (i) no solution ,(ii) a unique solution, (iii) an infinite number of solutions.
3) Show that the three equations
-2x+y+z=a, x-2y+z=b, x+y-2z=c
have no solutions unless a+b+c=0,in which case they have infinitely many solutions.Find these solutions when a=1,b=1,c= -2.
