Summary: Linear Algebra Worksheet 6
Math 108A Fall 2009, TA Grace Kennedy
Course Website: http://math.ucsb.edu/kgracekennedy/F09108A.html
Supplemental Reading: Axler Chapter 4
MIDTERM II REVIEW
The second midterm is cumulative. Some of these are problems from old
worksheets that you may or may not have gotten to finish. Get into groups and
work on problems you feel you need the most help on.
The calculation problems are at the end.
Let F be a field, and let V be a vector space of dimension n < over F. Unless
otherwise stated, all vector spaces are over this field F.
1 Fields and Vector Spaces
1. This statement is almost correct; correct and prove: Let r, r , and s F.
If rs = r s, then r = r .
This is called the cancelation property in fields.
2. Prove or disprove: If v, v , and w V , then v +w = v +w implies v = v .
3. True or False: The set of m×n matrices with entries in F is a vector space
over F. (Give a brief explanation for your answer.)
4. True or False: If W, W , and U are subspaces of V , then W +U = W +U