We will now write a function that solves a linear system $)=(b$ quickly, given a $LU$ decomposition of A with a right hand side vector $b.$ Create a function $($this will be added to the final submitted source file

HW$2.$py$)$ which is called solve LU$()$ that takes the following arguments as input in this order:

numpy array $L$ : the lower triangular matrix of an LU decomposition of A

numpy array $U$ : the upper triangular matrix of an LU decomposition of A

numpy array $b$ : the right hand side vector of the system $Ax=b$

And returns the following output:

numpy array $x$ : the solution to the original system $Ax=b$

Hints: This involves solving two simple systems, one with forward substitution then one with backward substitution. Do NOT use the built in solvers $($numpy$.$linalg.solve$())$