Investigate for what values of `lambda,mu` the simultaneous equations `x+y+z=6:x+2y+3z=100:x+2y+lambdaz=mu` have:

Investigate for what values of lambda, mu the simultaneous equations x + y + z = 6, x + 2 y + 3 z = 10 & x + 2 y + lambda z = mu have, An infinite number of solutions.

Investigate for what values of lambda, mu the simultaneous equations x + y + z = 6, x + 2 y + 3 z = 10 & x + 2 y + lambda z = mu have, A unique solution.

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 .

. For what values of lambda and mu the system of equations x+y+z=6, x+2y+3z=10, x+2y+lambdaz=mu has (i) Unique solution (ii) No solution (iii) Infinite number of solutions

. For what values of lambda and mu the system of equations x+y+z=6, x+2y+3z=10, x+2y+lambdaz=mu has (i) Unique solution (ii) No solution (iii) Infinite number of solutions

. For what values of lambda and mu the system of equations x+y+z=6,x+2y+3z=10,x+2y+lambda z=mu has (i) Unique solution (ii) No solution (iii) Infinite number of solutions

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.

Investigate the values of lambda and mu so that the equations 2x+3y+5z=9,7x+3y-2z=8,2x+3y+lambda.z=mu have (i) no solution,(ii)a anque solution and (iii)an infuute number of solutions

Find lambda and mu so that the simultaneous equations x+y+z= 6, x + 2y + 3z = 10, x + 2y + lambda z = mu have infinite number of solutions.