Back-substitution

Write a routine that solves a system after knowing its LU decomposition. Input arguments:

• , a compact decomposition, as computed by the routine at point 1.
• , teh integer vector of permutations, as computed by the routine at point 1.
• , a right hand vector.

Output arguments:

• , containing the solution of the system; the input value of is overwritten.

The header and the declarations of this routine should be

subroutine FB_Subst(A,b,Pivot)
implicit none
! The LU factorization, as given by LU_Fact
real, intent(in), dimension(:,:) :: A
! The RHS vector
real, intent(inout), dimension(:) :: b
! Vector of permutations, as given by LU_Fact
integer, dimension(:), intent(in)   :: Pivot
.....................................

The routines LU_Fact and FB_Subst will both be submitted in the same file, lin_solve.f90.