Math 3130
Spring 2016 Abrams
Exam 1 Information
This exam will happen on Thursday, March 10. It will last for the entire 75 minutes of the class period. This
exam will cover the material from Chapter 4, Sections 1,2,3,4,5,7,8. (So Section 6 will not be covered.) You
will need to know / review the material from Chapters 1 and 2 which appeared on Quiz 1. While there will be
no questions which are identical to quiz questions, you will need to know how to use the computational tools
contained on that quiz (e.g. solve linear systems, compute inverses of matrices, use determinants, etc ...)
I would suggest you read your notes to get a good ’big picture’ of what we have covered. Then review your
homework. For problems you think you are having trouble with, do a few more of the problems in each of the
assigned sections. ONLY THEN should you attempt the Practice Exam.
Solutions to the Practice Exam (as well as a blank copy of the Practice Exam, in case you’d like to print off
an extra copy) can be found at the course website
http://www.uccs.edu/∼gabrams/CourseMainPageMath3130Spring2016.html
Here are the things you should be able to do for this exam:
1. If you are given a ’known’ vector space, be able to prove that a given subset of that vector space is or is
not a subspace.
2. Recognize examples of vector spaces.
3. Know the definition of ’linear combination’, know what it means for a given set to span a vector space, and
know the definition of span(S) for a subset S of a vector space.
4. Be able to show that a specific vector is or is not a linear combination of the vectors in a given set.
5. Give a geometric interpretation of linear combinations in R3 .
6. Be able to show that a given set of vectors is or is not linearly independent.
7. Know the definition of a basis for a vector space. Be able to show that a given subset of a vector space is
or is not a basis.
8. Know the nice ’determinant trick’ for determining whether or not a set of n vectors in Rn is a basis of Rn .
9. Know the definition of the dimension of a vector space.
10. Know the definition of the row space, column space, and null space of a matrix A. Be able to compute
dimensions and bases for these. Be able to prove that the null space is a subspace of Rn .
11. Given a subspace of Rn spanned by a set of vectors, be able to find a basis for this subspace. (There are
two processes which can be used here, one which simply produces SOME basis, the other which produces a basis
consisting of vectors from the given set. Know how to complete both of these processes.)
12. Know the definition of the rank and nullity of a matrix. Know the statement/formula of the Dimension
Theorem for Matrices (you need not prove this). Be able to compute the rank and nullity of a given matrix.
13. There will be a few ’big picture’, general questions (probably short answer or true/false). These will be
clear from your notes and the lectures.
My office hours during the week of the exam are: Tuesday March 8 11:45 - 12:15, and 4:30 - 5:00; and Thursday
March 10 1:00 - 1:30. In addition, I will also be in on Wednesday March 9 from 3:00 - 3:30. My office is ENGR
288.
Also, remember:
- the Supplemental Instruction sessions with Ikko Saito: Tuesdays and Thursdays, 12:20 - 1:50pm, Columbine
Hall Room 105 and
- The Math Center, located in ENGR Room 233. Free drop-in tutoring. Hours for this semester are: Monday
- Thursday 8 am - 7 pm; Friday 8 am - 4:30 pm; Sunday 11 am - 3 pm.
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