(1) Prove that if two homogeneous systems of linear equations in two unknowns have the same solutions, then they are equivalent.
(2) Can you prove that the matrix
A = [1 1/2 ... 1/n
1/2 1/3 ...1/(n+1)
is invertible and that A^(-1) has integer entries?
(1) Perhaps the theorem - Equivalent systems of linear equations have the same solutions? It is the other way round.
(2)hmm...I don't know of "relevant equations"
The Attempt at a Solution
Not very sure how to start. For the first one, tried to construct arbitrary matrices A and B to represent two different homogeneous systems, but didn't get very far.
For (2), tried row-reducing the matrix > echelons but don't know how a proof will result...