For what value of `lambda`, the system of equations x+y+z=1, x+2y+4z=`lambda`, x+4y+10z=`lambda^(2)` is consistent

The system of equations x +2y+3z=1, x-y+4z=0, 2x+y+7z=1 has

The system of equations -2x+y+z=a x-2y+z=b x+y-2z=c has

The set of all values of lambda for which the system of linear equations x - 2y - 2z = lambdax x + 2y + z = lambday -x -y = lambdaz has a non-trivial 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 .

Find lambda for which the system of equations x+y-2z=0,2x-3y+z=0,x-5y+4z=lambda is consistent and find the solutions for all such values of lambdadot

Determine the values of lambda for which the following system of equations x+y+3z=0,4x+3y+ lambda z=0, 2x+y+2z=0 has (i) a unique solution (ii) a non-trivial solution.

Examine the consistency of the system of equations x+ y +z=1 2x+ 3y +2z =2 ax+ay +2az =4

Examine the consistency of the system of equations 3x-y -2z =2 2y - z =-1 3x- 5y =3