Enter$[$L$,$U$,$P$]=$ lu$($A$)$to find the LU factorization of the matrix PA$.$ Verify that $$by computing P$*$A$-$L$*$U$($assign this to variable ans$1).$

Use the LU factorization$$you found in part $(1)$ to solve the system : first use the $"\backslash "$ command to solve the system $($store the solution in the variable y$)$ and then solve the system $.$ Call the computed solution x$\_$lu$.$

The exact solution to the system $$is the vector $.$ Enter the vector x$$and compare your solution x$\_$lu from part $(2)$ with the exact solution x$$by computing norm$($x$\_$lu$-$x$)($assign this to variable ans$2)$