
Path To College Mathematics
1st Edition
ISBN: 9780134654409
Author: Martin-Gay, K. Elayn, 1955-
Publisher: Pearson,
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Question
Chapter D, Problem 8ES
To determine
The solution of the proportion
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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.
N Page
0.6.
0.4.
0.2-
-0.2-
-0.4-
-6.6
-5
W
10
Chapter D Solutions
Path To College Mathematics
Ch. D - Prob. 1ESCh. D - Prob. 2ESCh. D - Prob. 3ESCh. D - Prob. 4ESCh. D - Prob. 5ESCh. D - Prob. 6ESCh. D - Prob. 7ESCh. D - Prob. 8ESCh. D - Prob. 9ESCh. D - Prob. 10ES
Ch. D - Prob. 11ESCh. D - Prob. 12ESCh. D - Prob. 13ESCh. D - Prob. 14ESCh. D - Prob. 15ESCh. D - Prob. 16ESCh. D - Prob. 17ESCh. D - Prob. 18ESCh. D - Prob. 19ESCh. D - Prob. 20ESCh. D - Prob. 21ESCh. D - Prob. 22ESCh. D - Prob. 23ESCh. D - Prob. 24ESCh. D - Prob. 25ESCh. D - Prob. 26ESCh. D - Prob. 27ESCh. D - Prob. 28ESCh. D - Prob. 29ESCh. D - Prob. 30ESCh. D - Prob. 31ESCh. D - Prob. 32ESCh. D - Prob. 33ESCh. D - Prob. 34ESCh. D - Prob. 35ESCh. D - Prob. 36ESCh. D - Prob. 37ESCh. D - Prob. 38ESCh. D - Prob. 39ESCh. D - Prob. 40ESCh. D - Prob. 41ESCh. D - Prob. 42ESCh. D - Prob. 43ESCh. D - Prob. 44ESCh. D - Prob. 45ESCh. D - Prob. 46ESCh. D - Prob. 47ESCh. D - Prob. 48ES
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