Matrices and De...

Let a, b and c be any real numbers. If there are real numbers χ, y and z not all zero such that χ = cy + bz, y = az + cχ and z = bχ + ay have non - zero solution. Then, a² + b² + c² + 2abc is equal to

The system of equations χ + y + z = 0, 2χ + 3y + z = 0 and χ + 2y = 0 has

The systems of equations χ + y + z = 8, χ - y + 2z = 6 and 3χ + 5y - 7z = 14 has

If a, b and c are positive real numbers. The following system of equations

The simultaneous equations kχ + 2y - z = 1, (k - 1)y - 2z and (k + 2)z = 3 have only one solution, when

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

The system of equations 2χ + y - 5 = 0, χ - 2y + 1 = 0 and 2χ - 14y - a = 0 is consistent. Then, a is equal to

The values of λ and μ for which the system of equations χ + y + z = 6, χ + 2y + 3z = 10 and χ + 2y + λz = μ have infinite number of solutions, are