Class 12 Maths Notes: Determinants – Linear Equations using Determinants

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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