Determine whether the following equations will have non-trivial solutions, if so solve them: `x+3y-2z=0, 2x-y+4z=0,x-11y+14z=0`

Solve the system: x+3y-2z=0,2x-y+4z=0,x-11y+14z=0 .

Test whether the following system of equations have non zero solution. Write the solution set. 2x+3y+4z=0 x-2y-3z=0 3x+y-8z=0

Solve the system : 2x+3y-z=0, x+y+z=0, 2x+y+2z=0 .

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

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

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.

Solve the system of equations x+3y -2z =0, 2x-y+4z =0 ,x-11y+14z =0