Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
8th Edition
ISBN: 9781305279148
Author: Stewart, James, St. Andre, Richard
Publisher: Cengage Learning
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Chapter 4.9, Problem 2PT
To determine
To choose: The appropriate option for
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A factorization A = PDP 1 is not unique. For A=
7 2
-4 1
1
1
5 0
2
1
one factorization is P =
D=
and P-1
30
=
Use this information with D₁
=
to find a matrix P₁ such that
-
-1 -2
0 3
1
-
- 1
05
A-P,D,P
P1
(Type an integer or simplified fraction for each matrix element.)
Matrix A is factored in the form PDP 1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace.
30 -1
-
1 0 -1
400
0
0 1
A=
3 4 3
0 1 3
040
3 1 3
0 0
4
1
0
0
003
-1 0 -1
Select the correct choice below and fill in the answer boxes to complete your choice.
(Use a comma to separate vectors as needed.)
A basis for the corresponding eigenspace is {
A. There is one distinct eigenvalue, λ =
B. In ascending order, the two distinct eigenvalues are λ₁
...
=
and 2
=
Bases for the corresponding eigenspaces are {
and ( ), respectively.
C. In ascending order, the three distinct eigenvalues are λ₁ =
=
12/2
=
and 3 = Bases for the corresponding eigenspaces are
{}, }, and {
respectively.
Chapter 4 Solutions
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Ch. 4.1 - Prob. 1PTCh. 4.1 - Sometimes, Always, or Never: If f(c) = 0, then c...Ch. 4.1 - The critical numbers of f(x) = 3x4 = 20x3 36x2...Ch. 4.1 - Prob. 4PTCh. 4.1 - True or False: The absolute extrema of a...Ch. 4.1 - Prob. 6PTCh. 4.1 - Prob. 7PTCh. 4.2 - Prob. 1PTCh. 4.2 - Prob. 2PTCh. 4.2 - Prob. 3PT
Ch. 4.2 - True or False: If f(x) = g(x) for all x then f(x)...Ch. 4.2 - Prob. 5PTCh. 4.3 - Prob. 1PTCh. 4.3 - Prob. 2PTCh. 4.3 - Prob. 3PTCh. 4.3 - Prob. 4PTCh. 4.3 - Prob. 5PTCh. 4.3 - Prob. 6PTCh. 4.3 - True or False: If f(c) = 0, then c is a point of...Ch. 4.3 - Prob. 8PTCh. 4.3 - Prob. 9PTCh. 4.3 - Prob. 10PTCh. 4.4 - Prob. 1PTCh. 4.4 - Prob. 2PTCh. 4.4 - Prob. 3PTCh. 4.4 - limx(lnx)1/x= a) 0 b) 1 c) e d)Ch. 4.5 - Prob. 1PTCh. 4.5 - Prob. 2PTCh. 4.5 - Prob. 3PTCh. 4.5 - True or False: If f(x) 0 for all x in an interval...Ch. 4.5 - Prob. 5PTCh. 4.5 - Prob. 6PTCh. 4.5 - Prob. 7PTCh. 4.6 - Prob. 1PTCh. 4.6 - Prob. 2PTCh. 4.6 - Prob. 3PTCh. 4.7 - Prob. 1PTCh. 4.7 - A carpenter has a 10-foot-long board to mark off a...Ch. 4.7 - Prob. 3PTCh. 4.7 - Prob. 4PTCh. 4.8 - Prob. 1PTCh. 4.8 - Prob. 2PTCh. 4.8 - Prob. 3PTCh. 4.9 - Prob. 1PTCh. 4.9 - Prob. 2PTCh. 4.9 - Prob. 3PTCh. 4.9 - Prob. 4PTCh. 4.9 - Prob. 5PT
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