**CRAMER’S RULE**

*Example -: Prove that the system of the equations, 237x + 229y + 221z = 213,
– 3x + 7y+17z = 27 and 7x + 19y + 31 z = 43, have infinitely many solutions.*

** 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

*Example – : For what values of p and q, the system of equations *

* 2x + py + 6z = 8 *

* x + 2y + qz = 5 *

* x + y + 3z = 4 *

* Has
(i) no solution *

*(ii) a unique solution*

*(iii) infinitely many solutions*

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CBSE Class 12 Maths Determinants All Topic Notes CBSE Class 12 Maths All Chapters Notes

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