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# Cramer's Rule

##### This online calculator solves system of linear equations using Cramer's rule and shows detailed steps of the solution
Timur2016-10-13 21:25:03

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This online calculator solves system of linear equations using Cramer's rule and shows detailed steps of the solution - substituted matrixes and calculated determinants. Some theory is below the calculator, as usual.

##### Cramer's Rule
Solution steps:

Cramer's rule can be used for systems of linear equations where the number of equations is equal to the number of unknown variables and coefficient matrix's determinant is not zero (otherwise system of equations does not have unique solution - either it has no solution at all or it has infinite or parametric solution, and you have to use other methods to find it).

System of linear equations in matrix form looks like this
$AX=B$

If system of linear equations satisfies abovementioned conditions, it has the only solution $(x_{1}, x_{2}, ... , x_{n})$, which can be expressed using this formula
$x_{i} = \frac{\Delta_{A_i}}{\Delta_A}$,
where $\Delta_{A_i}$ – determinant formed by replacing the x-column values with the answer column (B) values, and $\Delta_A$ – coefficient matrix's determinant.

This is Cramer's rule. In fact, it is a handy way to solve for just one of the variables without having to solve the whole system of equations.

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