University of Toronto at Scarborough
Department of Computer & Mathematical Sciences
MATA33
Assignment 5
Winter 2008
Quiz 5 is based on this assignment and the relevant text readings and lecture notes.
Quiz 5 will
be written in the 6th tutorial, which takes place during the week of Feb. 25  29.
Study:
Lecture notes on determinants. A nice OnLine reference for determinants (and other topics
on matrices) is
http://distanceed.math.tamu.edu/Math640/chapter1/node9.html
Review our text and lecture material from Sections 6.1 6.6 as necessary.
Problems:
1. In all parts of this question, use the 2
×
2 matrices
A
and
B
in Example 4 on page 235.
(a) Find
det
(
A
),
det
(
B
), and verify that
det
(
AB
) =
det
(
A
)
det
(
B
) and
det
(
A
T
) =
det
(
A
)
(b) Verify that
det
(
A
+
B
)
6
=
det
(
A
) +
det
(
B
)
(c) Verify that
det
(
A

1
) =
1
det
(
A
)
(d) If
C
is the 2
×
2 matrix obtained by multiplying the first row of
A
by a number
p
and
the second row of
A
by a number
q
, verify that
det
(
C
) =
pq
(
det
(
A
)).
(e) Find all real numbers
x
for which the matrix
xI

A
is invertible.
2. In all of this question, use the 3
×
3 matrices
A
and
B
given at the beginning of the Problems
Section 6.3 on page 248.
(a) Find
det
(
A
),
det
(
B
), and then verify that
det
(
AB
) =
det
(
A
)
det
(
B
).
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 G
 Math, Linear Algebra, Complex number, Det

Click to edit the document details