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Answers to your questions 03/08/10:
Administrative questions
1.
It is great that you have lecture notes for us to print out. We can follow you and it makes the
class easier.
Thanks for the comment. I appreciate it.
Questions on general topics
2.
When is it necessary to use elementary row operations in general?
We use them when doing GE.
3.
How frequently do 4x4 or larger matrices appear in practical applications of linear algebra?
Very frequently. You will see it if you go to applied mathematics field.
4.
What does consistent systems and inconsistent system has to do in section 3.3?
The system is inconsistent if it has no solution. There are all kinds of systems to solve.
5.
Determinant of a matrix tells us whether or not the matrix is independent. Does trace of a
matrix tell us anything about the matrix?
Good question. Sometimes trace is used in analysis of eigenvalues. It can also be used in finding
the expectation of quadratic forms.
6.
Does determinant tell us anything more other than linear dependency?
Good question. In Cramer’s rule, you can use it to find solution of equations. It is not
computationally easy, but it can be used in theoretical proofs. Potentially, it can be used to
analyze a matrix in order to design a good algorithm for solving certain system of equations.
7.
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 Winter '08
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 Linear Algebra, Algebra

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