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Basic Concepts Of Determinant Part 8

Posted on - 04-01-2017

Math

IIT JEE

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.

     
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