System of Three Linear Equations

Find the solutions to a system of three linear equations.

$\normalsize{\left[\begin{array}\\ a_{\small 11}& a_{\small 12}& a_{\small 13}\\ a_{\small 21}& a_{\small 22}& a_{\small 23}\\a_{\small 31}& a_{\small 32}& a_{\small 33}\\\end{array}\right]} {\left[\begin{array}\\ x_{\small 1}\\ x_{\small 2}\\x_{\small 3}\\\end{array}\right]}={\left[\begin{array}\\ b_{\small 1}\\ b_{\small 2}\\b_{\small 3}\\\end{array}\right]}\\ $

_{(Click on each cell in the matrix to enter values)}

Matrix A
{aij}

_i＼^j	1	2	3
1
2
3

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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