The system of homogeneous simultaneous linear equations
a1x + b1y + c1z = 0; a2x + b2y + c2z=0; a3x + b3y + c3z=0
has a non-trivial solution (i.e. at least one of x,y,z, is different from zero ) if
Example -: If the system of equations 3x + 10 y + 17z = 0, –x + 6 y + 13 z = 0 and
20 x – 13y + l z = 0 has a non-trivial solution then find the solution.
Solution: The observation for A.P. property reveals l = -46 to have D = 0 (non-trivial solution)
Let z = k and by first two equations, we have
3x +10 y = – 17 k
–3x + 18y = – 39 k, therefore y = – 2k and x = k
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