HOMEWORK 8.
Due Monday, November 14, in class.
1. Let Vbe an inner product space, let xi∈V, 1 ≤i≤n, and let Abe an
n×nmatrix such that Aij =hxi, xji. Prove that vectors xi, 1 ≤i≤n, are
linearly independent if and only if Ais invertible.
2. Do Problem 8 in Section 6.1.
3. Do Problem 25 in Section 6.1.
4. Do Problem 12 in Section 6.2.
5. Do Problem 18 in Section 6.2.