Find the value of c for which the following equations have non trivial solutions `cx-y-z=0` `-cx+y-cz=0` `x+y-cz=0` (A) `(1)/(2)` (B) `-1` (C) `2` (D) 0

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

Show that in general there are three values of t for which the following system of equations has a non- trival solution (a-t)x+by+cz=0, bx+(c-t)y+az=0 and cx+ay+(b-t)z=0. Express the product of these values of t in the form of a determinant.

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

Find the real values of r for which the following system of linear equations has a non-trivial solu- tions. Also find the non-trivial solutions 2rx – 2y + 3z = 0 x + r y + 2z = 0 2x + r z = 0

The greatest value of c in R for which the x-cy-cz=0 system of linear equations cx-y+cz,=0 has a non-trival solution,is:

Find the real values of lambda for which the following system of linear equations has non- trivial solutions.Also,find the non-trivial solutions.2 lambda x-2y+3z=0x+lambda y+2z=02x+lambda z=0

The greatest value of c in R for which the system of linear equations x-cy-cz = 0, cx -y + cz =0, cx + cy-z =0 has a non-trivial solution, is