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 `"____"`

Show that the equations 3x+y+9z=0, 3x+2y+12z=0 and 2x+y+7z=0 have non-trival solutions also.

The values of k in R for which the system of equations x+k y+3z=0,k x+2y+2z=0,2x+3y+4z=0 admits of nontrivial solution is 2 b. 5//2 c. 3 d. 5//4

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

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

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.

The minimum value of P=b c x+c a y+a b z , when x y z=a b c , is

Test the consistency of the linear equations 3x-y+z=3 , 2x+2y-3z=1 and 25x+5y-10z=20 .

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 .

If the system of equation {:(,x-2y+z=a),(2x+y-2z=b),and,(x+3y-3z=c):} have at least one solution, then

The number of values of k for which the linear equations 4x""+""k y""+""2z""=""0 k x""+""4y""+""z""=""0 2x""+""2y""+""z""=""0 posses a non-zero solution is : (1) 3 (2) 2 (3) 1 (4) zero