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Cramer's Rule Calculator

Here you can solve systems of simultaneous linear equations using Cramer's Rule Calculator with complex numbers online for free with a very detailed solution. The key feature of our calculator is that each determinant can be calculated apart and you can also check the exact type of matrix if the determinant of the main matrix is zero.

Have questions? Read the instructions.

Matrix dimension:   

About the method

To solve a system of linear equations using Cramer's rule algorithm you need to do the following steps.

  1. Set an augmented matrix.
  2. Calculate a determinant of the main (square) matrix.
  3. To find the 'i'th solution of the system of linear equations using Cramer's rule replace the 'i'th column of the main matrix by solution vector and calculate its determinant. Then divide this determinant by the main one - this is one part of the solution set, determined using Cramer's rule. Repeat this operation for each variable.
  4. If the main determinant is zero the system of linear equations is either inconsistent or has infinitely many solutions. Unfortunately it's impossible to check this out exactly using Cramer's rule. Gauss-Jordan elimination calculator will help you.

To understand Cramer's rule algorithm better input any example and examine the solution.

Matrix input