Gaussian vs Cramer’s vs Kronecker-Capelli Methods – Matrices in Solving Systems of Linear Equations
Krystian Karczyński
Founder and General Manager of eTrapez.
Graduate of Mathematics at Poznan University of Technology. Mathematics tutor with many years of experience. Creator of the first eTrapez Courses, which have gained immense popularity among students nationwide.
He lives in Szczecin, Poland. He enjoys walks in the woods, beaches and kayaking.
The need to solve systems of equations for an increasing number of equations and unknowns has effectively propelled the study of matrices as such, starting as far back as ancient Babylon and China.
Methods for Solving Systems of Linear Equations
We can solve a system of linear equations just as well:
– using Cramer’s method in conjunction with the Kronecker-Capelli Theorem
– using Gauss’s method
I must say, Gauss’s method has a definite advantage. Not just because of its universality (Cramer and Kronecker-Capelli can also deal with any system), but because of the relative ease of computation. It doesn’t require calculating determinants, which becomes significant when dealing with systems of, say, 10 equations and 12 unknowns…
Therefore, I really recommend Gauss!
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