The system of equations `2x^2-3y^2+z^2+6=0, x^2-7y^2-2z^2-5=0` and `5x^2-y^2+4z^2+23=0` has

The system of equations x-2y+3z=5, 2x-2y+z=0, -x+2y-3z=6 has

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

If the system of equations 2x-3y+4z=0, 5x-2y-z=0 and 21x-8y+lamdaz=0 has non trival solution lamda is

Solve the following systems of linear homogenous equations : 3x+2y+7z=0 , 4x-3y-2z=0 and 5x+9y+23z=0

The equations 2x-3y+6z=4, 5x+7y-14z=1 3x+2y-4z=0, have

The system of equations lambda x + y + 3z = 0, 2x + mu y - z = 0, 5x + 7y + z = 0 has infinitely many solutions in R. Then,

If (x_(0), y_(0), z_(0)) is any solution of the system of equations 2x-y-z=1, -x-y+2z=1 and x-2y+z=2 , then the value of (x_(0)^(2)-y_(0)^(2)+1)/(z_(0)) (where, z_(0) ne 0 ) is

If (x_(0), y_(0), z_(0)) is any solution of the system of equations 2x-y-z=1, -x-y+2z=1 and x-2y+z=2 , then the value of (x_(0)^(2)-y_(0)^(2)+1)/(z_(0)) (where, z_(0) ne 0 ) is