Cramer's Rule
- If any
of Dx, Dy, Dz ∈ R and D
>
0, system of equation have unique solution and called consistence
independent.
- If Dx = Dy= Dz = 0 and D
is also zero then the system of equation have infinity many solution and
called consistence dependent.
- If atleast one of Dx, Dy, Dz is non zero and D
is zero, then the system of equations have no solution and called inconsistant.
Example.1
Prove that the system of the
equations have infinitely many solutions:
237x + 229y + 221z = 213
–3x + 7y + 17 z = 27
7x + 19y + 31 z = 43..
Solution
Coefficient of variable and the
constant in the right hand side in each equation are in A.P. with
different common difference 8, 10 , 12 respectively therefore D1 = Dx = Dy =Dz = 0 and hence system of equation
have infinitely many solution.
