This preview shows pages 1–2. Sign up to view the full content.
AMS 210.03
David Fried
Test 1
B
Name_________________________________
No calculators are permitted.
Complicated arithmetic expressions may be left as is and need not be
evaluated.
1.
The matrix
A
=
2
5
6
1
±
has eigenvectors
u
1
=[1,1] and
u
2
=[5,6]
a)
What are the corresponding eigenvalues
λ
1
and
λ
2
? (10 points)
b)
Write the vector
v
=[7,15] as a linear combination of
u
1
and
u
2
. (10 points)
c)
Use your result from (b) to determine
A
10
v
. (5 points)
2.
Let the matrices
A
and
B
and the vectors
x
and
y
be given by:
A
=
1
0
3
1
0
2
2
0
±
B
=
−
3
0
1
2
±
x
=[1,1]
y
=[3,0,2]
a)
Which of the following products are possible (you need not compute them and you may use
the vectors as either row vectors or column vectors)? (5 points)
x∙y, AB, BA, xA, Ax, yB, Ay
b)
Perform one of the possible multiplications from part (a). (5 points)
3.
Consider the following growth model for the interaction between caterpillars and wasps in a garden:
C′
W′
±
=
1.3
−
.5
.5
.8
±
C
W
±
What vector norm measures the total bug population?
Use the corresponding matrix norm to
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.
 Fall '08
 FRIED
 Eigenvectors

Click to edit the document details