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Exam Review Sheets
Here is a link to some old exams.
- Test 1 is on Monday, July 3. It covers Chapters 1 & 2
plus any handouts (Lines & Planes, Vector Spaces,
the Maple worksheets (the mathematics not the notation), ...);
and Homework Sets 1-11. There will be two proofs. They
will be taken from this list.
- A(B+C) = AB + AB (see page 17 of your textbook)
- (AB)T = BTAT (see page 23)
- Derive via row operations the formula for the inverse
of a 2 x 2 matrix.
- The span of a set of vectors is a vector space.
(See Thm 4 on page 111. I did this in class a little differently.
The text uses Thm 3 on page 108, while I did it directly from
Thm 1 on page 103. Either way is fine.)
- Let V be a vector space and let W be a subspace
of V. Prove that if dim(W) = dim(V),
then W=V.
- Test 2 covers Chapter 3, Sections 4.1, 4.2, 5.1, 5.2 and 5.4;
homework sets 12-20. There will be two proofs. They
will be taken from this list.
- Thm 1 pg 207.
- Thm 2 pg 208.
- Thm 3 pg 209.
- Thm 5 pg 217.
- Thm 1 pg 317.
- Final covers everything.
There will be two or three proofs. They
will be taken from this list.
- Thm 3 pg 209.
- Thm 5 pg 217.
- Thm 1 pg 317.
-
- (AB)T = BTAT (see page 23)
- A vector space must contain a zero element. (Vector Space Handout)
- A vector space has a single zero element. (Vector Space Handout)