Summary: Math 2090 Spring 2005
Sections 4 and 7 P. Achar
Hour Exam 3 Solutions
April 12, 2005
Total points: 100 Time limit: 50 minutes
No calculators permitted. You must show all your work to receive full credit.
IMPORTANT: You must answer Problems 15 and Problem 11. For Problems 610, choose three out
of the five to answer. Note: in order to do Problem 11, you must answer at least one of Problems 9 or 10.
1. (4 points) What is the definition of dimension?
Solution: the number of vectors in a basis for the vector space
2. (6 points) Let v1, v2, v3, v4 be vectors in a vector space V . In each of the following situations, what
can you conclude about the dimension of V ? Your answers may be inequalities like "dim V 2,"
precise answers like "dim V = 5,", or the words "no information."
(a) v1, v2, v3, v4 are linearly dependent.
Solution: no information
(b) v1, v2, v3 span V .
Solution: dim V 3
(c) v1, v3, and v4 span V and are linearly independent.
Solution: dim V = 3
3. (12 points) Consider the linear transformation T : P2 R, T(p(x)) =