Review Sheet for Test II, Fall 2015
Colorado State University, Pueblo
Math 207 — Matrix and Vector Algebra with Applications
Terms [and concepts] you should know -- be able to state clearly what they
mean, recognize them in examples, and create your own examples of them:
- Gaussian elimination and Gauss-Jordan elimination
- elementary [row] operations
- solution sets of linear systems which are empty, have a single
point, or an infinite number of points — geometric interpretation
- row-equivalent matrices
- row-echelon form [REF] and reduced row-echelon form [RREF]
- the inverse of an $n\times n$ matrix
- how to find the inverse of a matrix by row-reducing a larger (wider)
matrix
- using the inverse of a the coefficient matrix of a linear system to solve
the system (maybe with several different right-hand sides)
- a linear combination of some vectors
- the span of some vectors
- linearly dependent and independent sets of vectors
- a basis of a subspace of $\RR^n$
- the null space $\operatorname{null}(A)$ of a matrix
- the range $\operatorname{range}(A)$ of a matrix
- determinants of $2\times 2$ and $3\times 3$ matrices
- the cross product of vectors in $\RR^3$: how to compute it, a
formula for its magnitude, and its orthogonality property
Format of the test
There will be problems similar to the homework, mini- and maxi-quizzes. There
will also be some problems which ask you to synthesize the computations and
perspectives of different parts of the material we've covered.
Total points on the test will be more than 100, but your maximum score will be
limited to 100; this means that you can choose which parts of the test to do
and still get a perfect score. If you do earn more than 100 points, the extra
points will be kept as course extra credit.
No book or notes will be permitted. Calculators will be permitted, and will
perhaps be useful. In particular, there will be likely be problems in which it
would be nice to compute the RREF form of a matrix quickly and accurately.
There will also surely be some computations with vectors and matrices which
you will have to do by hand since they will have symbols or irrational numbers
in the vectors and matrices.
How to prepare for the test
Make sure you are completely caught up on the homeworks and quizzes, and that
you now know how to do all those problems without trouble and with complete and
clear explanation of your work. Be aware that there could be problems which are
quite similar to the computations in homeworks and quizzes but which are a bit
more concept-based ... so it is important to know the how (and
to know how to explain it) for all the computations you can do.