Find the value of k for which the equations kx-2y+z=1, x-2ky+z=-2,x-2y+kz=1 have
(i) no solution
(ii) unique solution
(iii) infinitely many solution

For what values of p and q the system of equations 2x+py+6z=8, x+2y+qz=5, x+y+3z=4 has i no solution ii a unique solution iii in finitely many solutions.

For what values of k, the system of equations kx+y+z=1,x+ky+z=1,x+y+kz=1 have (i) unique solution (ii) more than one solution, (iii) no solution.

In vestigate the values of lambda and mu the system of linear equations 2x+3y+5z=9,7x+3y-5z=8, 2x+3y+ lambda z= mu , have (i) no solution (ii) a unique solution (iii) an infinite number of solutions.

For what value of mu the equations. x+y+3z=0,4x+3y+muz=0,2x+y+2z=0 have a (i) trivial solution (ii) non-trivial solution.

The system of equations -2x+y+z=a , x-2y+z=b , x+y-2z=c , has: (a)no solution if a+b+c!=0 (b)unique solution if a+b+c=0 (c)infinite number of solutions if a+b+c=0 (d)none of these

Investigate for what values of lambda and mu the system of linear equations. x + 2y + z = 7, x + y + lambda z = mu , x + 3y - 5z = 5 . Has (i) no solution (ii) a unique solution (iii) an infinte number of solutions. (b) P prpresents the variable complex number z. Find the locus of P , if Re ((z+1)/(z+i)) = 1 .

the sum of values of p for which the equations x+y+z=1x+2y +4z=p and x+4y +10z = p^(2) have a solution is "____"