a Write a Python function for computing the LU factorization of a general $\backslash ($ n $\backslash$times n $\backslash )$ matrix. The function call should look like

function $\backslash ([$L$,$ U$]=\backslash )$ lufactors$($A$)$

Test the code on a few examples and show the results.

b Write a Python function for the solution of a lower triangular system by forward substitution. The function call should look like

function $[$y$]=$ forwardsubst$($L$,$b$)$

Test the code on a few examples and show the results.

c Write a Python function for the solut ion of an upper triangular system by back substitution. The function call should look like

function $\backslash ([$x$]=\backslash )$ backsubst$(\backslash ($ U$,$ y$)\backslash )$

Test the code on a few examples and show the results.