Custom Kreyszig: Advanced Engineering Mathematics
10th Edition
ISBN: 9781119166856
Author: Kreyszig
Publisher: JOHN WILEY+SONS INC.CUSTOM
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DETAILS
MY NOTES
LARLINALG8 6.4.013.
Let B = {(1, 3), (-2, -2)} and B' = {(−12, 0), (-4, 4)} be bases for R², and let
42
- [13]
A =
30
be the matrix for T: R² R² relative to B.
(a) Find the transition matrix P from B' to B.
6
4
P =
9
4
(b) Use the matrices P and A to find [v] B and [T(V)] B, where
[v]B[31].
26
[V] B =
->
65
234
[T(V)]B=
->
274
(c) Find P-1 and A' (the matrix for T relative to B').
-1/3
1/3
-
p-1 =
->
3/4
-1/2
↓ ↑
-1
-1.3
A' =
12
8
↓ ↑
(d) Find [T(v)] B' two ways.
4.33
[T(v)]BP-1[T(v)]B =
52
4.33
[T(v)]B' A'[V]B' =
52
目
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DETAILS
MY NOTES
LARLINALG8 7.2.001.
1. [-/2.85 Points]
Consider the following.
-14 60
A =
[
-4-5
P =
-3 13
-1 -1
(a) Verify that A is diagonalizable by computing P-1AP.
P-1AP =
具首
(b) Use the result of part (a) and the theorem below to find the eigenvalues of A.
Similar Matrices Have the Same Eigenvalues
If A and B are similar n x n matrices, then they have the same eigenvalues.
(11, 12) =
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2. [-/2.85 Points]
DETAILS
MY NOTES
LARLINALG8 7.2.007.
For the matrix A, find (if possible) a nonsingular matrix P such that P-1AP is diagonal. (If not possible, enter IMPOSSIBLE.)
P =
A =
12 -3
-4
1
Verify that P-1AP is a diagonal matrix with the eigenvalues on the main diagonal.
P-1AP =
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3. [-/2.85 Points]
DETAILS
MY NOTES
LARLINALG8 7.1.021.
Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding eigenspaces) of the matrix.
2 -2 5
0 3 -2
0-1 2
(a) the characteristic equation
(b) the eigenvalues (Enter your answers from smallest to largest.)
(1, 2, 13) =
·( )
a basis for each of the corresponding eigenspaces
X1
x2
=
x3 =
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LARLINALG8 7.1.041.
Find the eigenvalues of the triangular or diagonal matrix. (Enter your answers as a comma-separated list.)
λ=
1 0 1
045
002
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Chapter 20 Solutions
Custom Kreyszig: Advanced Engineering Mathematics
Ch. 20.1 - Prob. 1PCh. 20.1 - Prob. 2PCh. 20.1 - Prob. 3PCh. 20.1 - Prob. 4PCh. 20.1 - Prob. 5PCh. 20.1 - Prob. 6PCh. 20.1 - Prob. 7PCh. 20.1 - Prob. 8PCh. 20.1 - Prob. 9PCh. 20.1 - Prob. 10P
Ch. 20.1 - Prob. 11PCh. 20.1 - Prob. 12PCh. 20.1 - Prob. 13PCh. 20.1 - Prob. 14PCh. 20.1 - Prob. 15PCh. 20.1 - Prob. 16PCh. 20.2 - Prob. 1PCh. 20.2 - Prob. 2PCh. 20.2 - Prob. 3PCh. 20.2 - Prob. 4PCh. 20.2 - Prob. 5PCh. 20.2 - Prob. 7PCh. 20.2 - Prob. 8PCh. 20.2 - Prob. 9PCh. 20.2 - Prob. 10PCh. 20.2 - Prob. 11PCh. 20.2 - Prob. 12PCh. 20.2 - Prob. 13PCh. 20.2 - Prob. 15PCh. 20.2 - Prob. 16PCh. 20.2 - Prob. 17PCh. 20.2 - Prob. 18PCh. 20.2 - Prob. 19PCh. 20.2 - Prob. 20PCh. 20.3 - Prob. 1PCh. 20.3 - Prob. 2PCh. 20.3 - Prob. 3PCh. 20.3 - Prob. 4PCh. 20.3 - Prob. 5PCh. 20.3 - Prob. 6PCh. 20.3 - Prob. 7PCh. 20.3 - Prob. 8PCh. 20.3 - Prob. 9PCh. 20.3 - Prob. 10PCh. 20.3 - Prob. 11PCh. 20.3 - Prob. 12PCh. 20.3 - Prob. 14PCh. 20.3 - Prob. 15PCh. 20.3 - Prob. 16PCh. 20.3 - Prob. 17PCh. 20.3 - Prob. 18PCh. 20.3 - Prob. 19PCh. 20.3 - Prob. 20PCh. 20.4 - Prob. 1PCh. 20.4 - Prob. 2PCh. 20.4 - Prob. 3PCh. 20.4 - Prob. 4PCh. 20.4 - Prob. 5PCh. 20.4 - Prob. 6PCh. 20.4 - Prob. 7PCh. 20.4 - Prob. 8PCh. 20.4 - Prob. 9PCh. 20.4 - Prob. 10PCh. 20.4 - Prob. 11PCh. 20.4 - Prob. 12PCh. 20.4 - Prob. 13PCh. 20.4 - Prob. 14PCh. 20.4 - Prob. 15PCh. 20.4 - Prob. 16PCh. 20.4 - Prob. 17PCh. 20.4 - Prob. 18PCh. 20.4 - Prob. 19PCh. 20.4 - Prob. 20PCh. 20.4 - Prob. 21PCh. 20.4 - Prob. 22PCh. 20.5 - Prob. 1PCh. 20.5 - Prob. 2PCh. 20.5 - Prob. 3PCh. 20.5 - Prob. 4PCh. 20.5 - Prob. 5PCh. 20.5 - Prob. 6PCh. 20.5 - Prob. 7PCh. 20.5 - Prob. 8PCh. 20.5 - Prob. 9PCh. 20.5 - Prob. 10PCh. 20.5 - Prob. 11PCh. 20.5 - Prob. 12PCh. 20.5 - Prob. 13PCh. 20.7 - Prob. 1PCh. 20.7 - Prob. 2PCh. 20.7 - Prob. 3PCh. 20.7 - Prob. 4PCh. 20.7 - Prob. 5PCh. 20.7 - Prob. 6PCh. 20.7 - Prob. 7PCh. 20.7 - Prob. 8PCh. 20.7 - Prob. 9PCh. 20.7 - Prob. 10PCh. 20.7 - Prob. 11PCh. 20.7 - Prob. 12PCh. 20.7 - Prob. 13PCh. 20.7 - Prob. 14PCh. 20.7 - Prob. 15PCh. 20.7 - Prob. 16PCh. 20.7 - Prob. 17PCh. 20.7 - Prob. 18PCh. 20.7 - Prob. 19PCh. 20.7 - Prob. 20PCh. 20.8 - Prob. 1PCh. 20.8 - Prob. 2PCh. 20.8 - Prob. 3PCh. 20.8 - Prob. 4PCh. 20.8 - Prob. 5PCh. 20.8 - Prob. 6PCh. 20.8 - Prob. 7PCh. 20.8 - Prob. 8PCh. 20.8 - Prob. 9PCh. 20.8 - Prob. 10PCh. 20.8 - Prob. 11PCh. 20.9 - Prob. 1PCh. 20.9 - Prob. 2PCh. 20.9 - Prob. 3PCh. 20.9 - Prob. 4PCh. 20.9 - Prob. 5PCh. 20.9 - Prob. 6PCh. 20.9 - Prob. 7PCh. 20.9 - Prob. 8PCh. 20 - Prob. 1RQCh. 20 - Prob. 2RQCh. 20 - Prob. 3RQCh. 20 - Prob. 4RQCh. 20 - Prob. 5RQCh. 20 - Prob. 6RQCh. 20 - Prob. 7RQCh. 20 - Prob. 8RQCh. 20 - Prob. 9RQCh. 20 - Prob. 10RQCh. 20 - Prob. 11RQCh. 20 - Prob. 12RQCh. 20 - Prob. 13RQCh. 20 - Prob. 14RQCh. 20 - Prob. 15RQCh. 20 - Prob. 16RQCh. 20 - Prob. 17RQCh. 20 - Prob. 18RQCh. 20 - Prob. 19RQCh. 20 - Prob. 20RQCh. 20 - Prob. 21RQCh. 20 - Prob. 22RQCh. 20 - Prob. 23RQCh. 20 - Prob. 24RQCh. 20 - Prob. 25RQCh. 20 - Prob. 26RQCh. 20 - Prob. 27RQCh. 20 - Prob. 28RQCh. 20 - Prob. 29RQCh. 20 - Prob. 30RQCh. 20 - Prob. 31RQCh. 20 - Prob. 32RQCh. 20 - Prob. 33RQCh. 20 - Prob. 34RQCh. 20 - Prob. 35RQCh. 20 - Prob. 36RQCh. 20 - Prob. 37RQCh. 20 - Prob. 38RQCh. 20 - Prob. 39RQCh. 20 - Prob. 40RQ
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