Implement a computer program which, for a given lower triangular matrix A with the diagonal entries different from zero,finds the matrix inverse to A by solving the equations Axj= ej for j=1,...,n by the " forward substitution"

Implement a compter program which decides whether a given matrix A e Mn is symmetric positive definite.

Implement a computer program which, for a band matrix A eMn with p=3=q such that the non zero elements ofA appear in the main diagonal and in the diagonals on the boundary of the band only,for a vector b e Rn and for w e(0,2), e>0 given, approximates the solution of the system Ax=b by the relaxation with accuracy e.