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6.5
Which, if either, of the following matrices corresponds to an area preserving transformation?
A
=
h
2

3
1
3
i
B
=
h
2

3
1
3
i
.
SOLUTION
We compute the magniﬁcation factor for each of these matrices, and see
whether it is 1 or not. By Theorem 16, the magniﬁcation factor of
±
a
b
c
d
²
is

ab

cd

.
Computing

ab

cd

for
A
we ﬁnd 9, so
A
is not area preserving. As written,
B
is the
same, so it is not area preserving. If however, we had
B
=
±
2
3
1
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Unformatted text preview: 1 ² , then we would have  abcd  = 1, so this would be an example of an area preserving matrix. 6.7 Let A = h 1 2 3 4 i . By the results of problem 1.6.6, the image of the unit circle under A is an ellipse. Find the equation of the ellipse and graph it. SOLUTION By the results of the previous problem, the equation of the ellipse is 25 u 2 + 5 v 222 uv = 4 . 21 /september/ 2005; 22:09 47...
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This note was uploaded on 10/03/2010 for the course MATH 380 taught by Professor Gladue during the Fall '08 term at Roger Williams.
 Fall '08
 Gladue
 Calculus, Matrices

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