http://interval.louisiana.edu/courses/362/spring2003math362_exam_hints.html
Math. 36201, Spring, 2003 Hints for the Exams
Instructor: R.
Baker Kearfott, Department
of Mathematics, University of Louisiana
at Lafayette
Office hours
and telephone, Email: rbk@louisiana.edu.
Home
page for the course
This page will change throughout the semester.
/ The
first exam / The
second exam / The
third exam / The
final exam /
Note: Previously given exams are available below
in Postscript format, that can be printed with a Postscript printer.
The files can also be viewed and printed with Ghostscript
and GSview.
The first exam:
This exam will be on Tuesday, February 11, and will be closed book.
You should find the exam fairly easy if you have studied the material collected
in class and also the homework that was collected on Tuesday, February
4. You should know how to do the following:

Write down the augmented matrix for a system of equations.

Put a system of equations (or its matrix) in reduced rowechelon form.

Determine the rank of a matrix.

Write down the solution set of s system of equations in terms of spanning
vectors and a translation vector.

Know about the dimension of the solution set of a system of equations,
and whether the solution set represents a line, plane, etc.

Know how to write down a system of linear equations in the form Ax =
b, where A is the matrix for the system, x is the vector
of unknowns, and b is the constant righthandside vector.
Postscript
copy of the first exam
PDF
copy of the first exam
First
exam answers
The second exam:
Postscript
copy of the second exam
PDF
copy of the second exam
Second
exam answers, page 1
Second
exam answers, page 2
The third exam:
The exam will be on Thursday, April 10, and will be closed book.
Besides looking over all of the homework and your notes from the class,
be sure to review the following:

How to write down a matrix for a linear transformation that maps the unit
square into a given parallelogram.

How to write down the matrix for a linear transformation that stretches
one or more coordinate axes.

How to write down the matrix for a linear transformation corresponding
to a rotation in a plane spanned by two of the coordinate axes.

How to interpret geometrically the product of two matrices.

How to compute the LU factorization of a matrix.

How to use the LU factorization of a matrix to solve a system of
equations.
Postscript
copy of the third exam
PDF
copy of the third exam
Third
exam answers, page 1
Third
exam answers, page 2
Answer
to bonus problem
The final exam:
The exam will be on Tuesday, May 13 at 7:30AM, and will be closed book.
You will need to be able to do the following:

Solve a system of equations by putting the system into reduced row echelon
form.

Solve a system of equations by producing, then using an LU factorization.

Compute the eigenvalues and eigenvectors of a matrix by writing down the
characteristic polynomial.

Compute a basis for the null space of a matrix and write down a basis for
the range.

Compute the QR factorization of a matrix.
Postscript
copy of the final exam
PDF
copy of the final exam
Final
exam answers, page 1
Final
exam answers, page 2
Final
exam answers, page 3
Final
exam answers, page 4