 # Hi ...plzzz explain how to apply Cramer's Rule and also demonstrates the technique.Thanx in advance!!!!

13 years ago

Given a system of linear equations, Cramer's Rule is a handy way to solve for just one of the variables without having to solve the whole system of equations. They don't usually teach Cramer's Rule this way, but this is supposed to be the point of the Rule: instead of solving the entire system of equations, you can use Cramer's to solve for just one single variable.

Let's use the following system of equations:

2x +   y + z = 3

x –   yz = 0

x + 2y + z = 0

We have the left-hand side of the system with the variables (the "coefficient matrix") and the right-hand side with the answer values. Let D be the determinant of the coefficient matrix of the above system, and let Dx be the determinant formed by replacing the x-column values with the answer-column values:

Cramer's Rule says that x = Dx ÷ D, y = Dy ÷ D, and z = Dz ÷ D. That is:

x = 3/3 = 1,  y = –6/3 = –2,  and  z = 9/3 = 3

That's all there is to Cramer's Rule. To find whichever variable you want (call it "ß" or "beta"), just evaluate the determinant quotient Dß ÷ D. (Please don't ask me to explain why this works. Just trust me that determinants can work many kinds of magic.)