Cramer's Rule

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Cramer’s Rule is a mathematical method used to solve a system of equations when the number of variables matches the number of equations. In the 1750s, mathematician Gabriel Cramer introduced this rule, which allows us to find the value of any variable without the need to calculate other values. Suppose, in the equations, there are 3 variables, such as x, y, and z. To find the value of z, we need to find the value of x and y first. Using Cramer’s rule, we can directly find the value of z without solving for the other variables. In this article, we will explore Cramer’s rule in detail.

Cramer's Rule for UK Students

What is Cramer’s Rule?

The technique used to solve systems of linear equations using determinants is called Cramer’s rule. The values of the variables can be determined by the determinants. Here, one determinant is derived from the number set in front of the variables, which is known as the coefficient matrix, and the other comes from changing one column from the matrix with the numbers following the equal signs (the answer column). After that, to find the value of a variable, divide the two determinants.

Let us see how Cramer’s rule works in the following system of equations:

2x + y + z = 3
x - y - z = 0
x + 2y + z = 0

Write the given equations with all coefficients:

2x + 1y + 1z = 3
1x - 1y - 1z = 0
1x + 2y + 1z = 0

Create the coefficient matrix and identify its determinant (D):

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.