" The number of non-trivial solutions of the system "x-y+z=0,x+2y=z=0;2x

The number of non trivial solutions of the system x-y+2=0,x+2y-z=0,2x+y+3z=0

The number of nontrivial solutions of the system: x-y+z=0, x+2y=0, 2x+y+3z=0 is

For what value of k, does the following system of equations possess a non-trivial solution over the set of rationals x+y-2z=0, 2x-3y+z=0 and x-5y+4z=k. Find all the solutions.

For what value of k, does the following system of equations possess a non-trivial solution over the set of rationals x+y-2z=0, 2x-3y+z=0 and x-5y+4z=k. Find all the solutions.

Write the number of solution of the following system of equation.x+y-z=0 3x-y+z=0 x-3y+z=0

Write the number of solution of the following system of equation. x+y+z=1 x+y+z=2 2x+3y+z=0

Find the real values of k for which the following system of linear equations has non-trivial solutions: x-ky+z=0,kx+3y-kz=0,3x+y-z=0