MA 52
May 13, 2006
Chapters 5,6,7 Review
SOLUTIONS PROBLEMS 1-20
Math 52 Spring 2006
0.5 0
2 1.5
1. (a) Express the matrix A =
as a product S DS 1 , where
D is a diagonal matrix.
1
0
(b) Find a formula for Ak
.
(a) By inspection, the eigenvalues are 1 = 0
Math 52
Midterm Review Solutions
(1) The reduced row-echelon form of the matrix representing this system is the
identity, so:
(a) Only x = 0, y = 0, z = 0.
(b) The system always has solutions.
(2) First recall that homogeneous means that the values on the
M A 52
May 9, 2006
Final Review
This packet contains review problems for the whole course, including all
the problems from the previous reviews. We also suggest below problems
from the textbo ok for chapters 5, 6, and 7. (Problems from earlier chapters
we
MA 52, Section 1
April 10, 2006
Quiz Review
Review your homework problems and their solutions rst! These are the
most helpful problems. Then, you can do problems from this review booklet,
or some in your text (for the text problems, I have suggested inter
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MA 52, Section 1
February 22, 2006
WORKSHEET
1. Find the inverse of the transformation obtained by rst rotating clockwise with angle /4 and then reecting about the line 7x1 + 24x2 = 0.
What happens if we rst reect and then rotate?
1
MA 52, Section 1
Febru
MA 52, Section 1
May 15, 2006
Review 2
Please do not make any assumptions about the composition of the nal
exam from this set of review problems. Do not assume that the exam questions will be exactly as the questions below, or slight modications of them.