1. If vectors in a real inner product space have equal length then are orthogona

1. If vectors in a real inner product space have equal length then are orthogonal. Prove it using the general properties of the inner product. 2. Show that eigenvalues of any real skew-symmetric (matrix are either 0 or pure imaginary. (Recall the proof of reality for the eigenvalues of a symmetric matrix modify it slightly) 3. Find the general solution of the system of course in real form