The equation `[1 2 2 1 3 4 2 4k][x y z]=[0 0 0]` has `a` solution for `(x ,y ,z)` besides `(0,0,0)dot` Then the value of `k` is _______.

The equation [(1,2,2),(1,3,4),(3,4,k)]=[(0),(0),(0)] has a solution for (x, y, z) besides (0, 0, 0). Then the value of k is _________ .

The equations x+y-2z=0,2x-3y-z=0,x-5y+4z=k have non-zero solutions if k=

If the system of equation 14x-3y+z=12, x-2y=0 and x+2z=0 has a solution (x_(0), y_(0), z_(0)) , then the value of x_(0)^(2)+y_(2)^(2)+z_(2)^(2) is equal to

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

The system of equations 6x+5y+ lamda z= 0, 3z-y+4z= 0, x+2y-3z=0 has non-trivial solutions for

If x=3k+2 and y = 2k-1 is a solution of the equation 4x-3y+1=0 , find the value of k.