System of Equations
Finds the solutions to a system of n equations.
| \(\normalsize{\left[\begin{array}\\ a_{\small 11}& a_{\small 12}& \cdots& a_{\small 1n}\\ a_{\small 21}& a_{\small 22}& \cdots& a_{\small 2n}\\ \vdots& \vdots& \ddots& \vdots\\a_{\small n1}& a_{\small n2}& \cdots& a_{\small nn}\\\end{array}\right]} {\left[\begin{array}\\ x_{\small 1}\\ x_{\small 2}\\ \vdots \\x_{\small n}\\\end{array}\right]}={\left[\begin{array}\\ b_{\small 1}\\ b_{\small 2}\\ \vdots \\b_{\small n}\\\end{array}\right]}\\ \) |
The solution x is obtained from the LU decomposition of matrix A using partial pivoting.
| \(\normalsize A{ x} =LU{ x}={ b}\\ { x}=A^{\small -1}{ b}=U^{\small -1}L^{\small -1}{ b}\\\) |
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