** Required reading:** Section 2.5-2.6, Section 3.1-3.3
(you can skip p.176-179)

Material covered this week: The matrix of a linear transformations,
matrix multiplicaion, change of bases, similarity transformations. Gauss elimination method, augmented matrices, elementary row operations.

Homework #6 is due 11pm on Monday, November 6

** Additional homework ** (do not hand in).
- Section 2.5, Problems 1,2b,2c,3c,3d,6a,7,8,10
- Section 2.6, Problems 1, 2, 4, 13, 14, 15, 16
- Section 3.1, Problems 1,2,6
- Prove that the dual space to $V=F^\infty_{fin}$ is $V^*=F^\infty$.
Show that the natural map $V\to (V^*)^*$ is not an isomorphism.