This WeekÕs Homework: Be sure to look over (but not turn) in 2.4 : 1,2,15,18 and 2.5:1,11,12.

Turn in 2.4: 3,4,5,8,12,17 and 2.5: 2(a,b,c),4,5,9 and the first and third exercises from the geometry hand out (Please rewrite any arguments found in our book in your own words. Also both these arguments work fine in infinite dimensions, unlike last week's exercise).

Note: The first problem was written dwon rather badly (I choos at the last moent to go from a vector space to itself rather than between vector spaces).

1. Let L be an isometry form (V,<-,->) to itself, then L preserves all inner-products, i.e.

$$\left< v,w \right> = \left<L(v),L(w) \right>.$$

Proposed Topics For this Week: Inverses, isomorphisms, and change of basis. Also winter carnival is Friday and we will have no class then.

The X-session Topic Proof madness! We will go through a variety of arguments and styles using actual examples from homework. Requests are welcome!. Just blitz me any problems that gave you trouble and we'll talk about them.