For which value (s) of `lambda`, do the pair of linear equations `lambdax + y = lambda^(2)` and `x + lambda y = 1 ` have
(i) no solution ? (ii) infinitely many solutions ?
(iii) a unique solution ?

For which value(s) of lamda , do the pair of linear equations lamda x+ y= lamda^(2) and x+ lamda y= 1 have no solution?

For which value(s) of lamda , do the pair of linear equations lamda x+ y= lamda^(2) and x+ lamda y= 1 have a unique solution?

For which value(s) of lamda , do the pair of linear equations lamda x+ y= lamda^(2) and x+ lamda y= 1 have infinitely many solutions?

For which value(s) of lambda do the pair of linear equations lambdax+y=lambda^(2)" and "x+lambday=1 have i] No solution? " " ii] Inifinitely many solutions? iii] A unique solution?

For which values of k, does the pair of linear equations kx+y=k^(2) and x+ky=1 have (1) no solution ? (2) infinitely many solutions? (3) a unique solution ?

The value of k, for which the pair of linear equations k x + y = k^(2) and x + k y = 1 has infinitely many solution, is :

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 .

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.