If the system of linear equations `x+y+3z=0,x+3y+k^(2)z=0,3x+y+3z=0` a non zero solution for some `k in R`,then `x+(y)/(z)=`

x+ky-z=0 , 3x-ky-z=0 and x-3y+z=0 has non-zero solution for k=

If the system of linear equations x+ky+3z=0 3x+ky-2z=0 2x+4y-3z=0 has a non-zero solution (x,y,z) then (xz)/(y^2) is equal to

Solve the system of equations 2x+3y-3z=0 , 3x-3y+z=0 and 3x-2y-3z=0

If the system of linear equations x-2y + kz = 1, 2x + y+ z = 2, 3x-y-kz = 3 has a solution (x, y, z), z ne 0 , then (x, y) lies on the straight line whose equation is

If the system of equations, 2x + 3y-z = 0, x + ky -2z = 0 " and " 2x-y+z = 0 has a non-trivial solution (x, y, z), then (x)/(y) + (y)/(z) + (z)/(x) + k is equal to

If x =a, y=b, z=c is a solution of the system of linear equations x + 8y + 7z =0, 9 x + 2y + 3z =0, x + y+z=0 such that point (a,b,c ) lies on the plane x + 2y + z=6, then 2a+ b+c equals

Show that the homogenous system of equations x - 2y + z = 0, x + y - z = 0, 3 x + 6y - 5z = 0 has a non-trivial solution. Also find the solution

The value of a for which the system of linear equations ax+y+z=0, ay+z=0,x+y+z = 0 possesses non-trivial solution is

The number of solutions of equations x + y - z=0, 3x - y - z= 0,x - 3y + z = 0 is

if the system of equations : {:(2x+3y-z=0),(3x+2y+kz=0),(4x+y+z=0):} have a set of non-zero integral solutions then , find the smallest positive value of z.