In the True or False questions below, give a simple justification. If true, justify by an argument/theorem; If False, give a counter-example; do not correct the statement.
1. The vectors (1+i, i) and (i, 1-i) in C² are orthogonal.
2. There is a normal matrix which is not Hermitian.
3. If two nonzero vectors in an IPS are orthogonal, then they are linearly independent.
4. In an IPS, if (x, y) = 0 for all x, then y = 0.
5. Every nonzero finite dimensional IPS has an orthonormal basis.
