## Gaussian Elimination

A method for solving Matrix Equations of the form

 (1)

Starting with the system of equations
 (2)

compose the augmented Matrix equation''
 (3)

Then, perform Matrix operations to put the augmented Matrix into the form
 (4)

Solve the equation of the th row for , then substitute back into the equation of the st row obtain a solution for , etc., according to the formula
 (5)

See also Gauss-Jordan Elimination, LU Decomposition, Matrix Equation, Square Root Method

© 1996-9 Eric W. Weisstein
1999-05-25