Gaussian Elimination Unraveled

Gaussian Elimination is a fundamental technique in linear algebra used to solve systems of linear equations by systematically reducing augmented matrices to their row-echelon or reduced row-echelon forms. This method involves a series of elementary row operations—such as adding multiples of one row to another or swapping rows—to transform the matrix into a triangular form, simplifying the process of finding solutions. Through this systematic elimination of variables, Gaussian Elimination paves the way for determining unique solutions, showing the dependency among equations, or identifying inconsistency in the system. Its elegance lies in its ability to streamline complex systems into a more manageable and interpretable form, making it a cornerstone in various fields, including mathematics, engineering, physics, and computer science.
#historyofmathematics #gausseliminationmethod

[askii]

this isn't even really true... gaussian elimination is only one of many many ways to solve and LU decomposition or Cholesky are the most commonly used techniques to do it numerically.