Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Chapter 2.8, Problem 19E
(a)
To determine
The differential equation for the mass.
(b)
To determine
The solution of the given differential equation.
(c)
To determine
The terminal velocity of the sinking mass from the given differential equation.
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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
67%
PREVIOUS ANSWERS
ill
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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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SUBMIT ANSWER
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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4. [-/2.85 Points]
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MY NOTES
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 2 Solutions
Advanced Engineering Mathematics
Ch. 2.1 - Prob. 1ECh. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.1 - Prob. 10E
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Prob. 25ECh. 2.4 - Prob. 26ECh. 2.4 - Prob. 27ECh. 2.4 - Prob. 28ECh. 2.4 - Prob. 29ECh. 2.4 - Prob. 30ECh. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Prob. 33ECh. 2.4 - Prob. 34ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.4 - Prob. 37ECh. 2.4 - Prob. 38ECh. 2.4 - Prob. 39ECh. 2.4 - Prob. 40ECh. 2.4 - Prob. 41ECh. 2.4 - Prob. 42ECh. 2.4 - Prob. 43ECh. 2.4 - Prob. 44ECh. 2.4 - Prob. 45ECh. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.5 - Prob. 9ECh. 2.5 - Prob. 10ECh. 2.5 - Prob. 11ECh. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Prob. 21ECh. 2.5 - Prob. 22ECh. 2.5 - Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - Prob. 27ECh. 2.5 - Prob. 28ECh. 2.5 - Prob. 29ECh. 2.5 - Prob. 30ECh. 2.5 - Prob. 31ECh. 2.5 - Prob. 32ECh. 2.5 - Prob. 33ECh. 2.5 - 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- [) Hwk 25 4. [-/4 Points] Hwk 25 - (MA 244-03) (SP25) || X Answered: Homework#7 | bartle X + https://www.webassign.net/web/Student/Assignment-Responses/last?dep=36606604 DETAILS MY NOTES LARLINALG8 6.4.019. Use the matrix P to determine if the matrices A and A' are similar. -1 -1 12 9 '-[ ¯ ¯ ], ^ - [ _—2—2 _ ' ], ^' - [ ˜³ −10] P = 1 2 A = -20-11 A' -3-10 6 4 P-1 = Are they similar? Yes, they are similar. No, they are not similar. Need Help? Read It SUBMIT ANSWER P-1AP = 5. [-/4 Points] DETAILS MY NOTES LARLINALG8 6.4.023. Suppose A is the matrix for T: R³ - → R³ relative to the standard basis. Find the diagonal matrix A' for T relative to the basis B'. A' = -1 -2 0 A = -1 0 0 ' 0 02 B' = {(−1, 1, 0), (2, 1, 0), (0, 0, 1)} ☐☐☐ ↓ ↑ Need Help? Read It Update available →] - restart now ASK YOUR T Sync and save data { Sign In ill ↑ New tab HT New window N New private window +HP ASK YOUR T Bookmarks History Downloads > > HJ Passwords Add-ons and themes HA Print... HP Save page as... HS…arrow_forwardClarification: 1. f doesn’t have REAL roots2. f is a quadratic, so a≠0arrow_forward[J) Hwk 25 Hwk 25 - (MA 244-03) (SP25) || X Answered: Homework#7 | bartle X + https://www.webassign.net/web/Student/Assignment-Responses/last?dep=36606604 1. [-/4 Points] DETAILS MY NOTES Find the matrix A' for T relative to the basis B'. LARLINALG8 6.4.003. T: R² → R², T(x, y) = (x + y, 4y), B' = {(−4, 1), (1, −1)} A' = Need Help? Read It Watch It SUBMIT ANSWER 2. [-/4 Points] DETAILS MY NOTES LARLINALG8 6.4.007. Find the matrix A' for T relative to the basis B'. T: R³ → R³, T(x, y, z) = (x, y, z), B' = {(0, 1, 1), (1, 0, 1), (1, 1, 0)} A' = ↓ ↑ Need Help? Read It SUBMIT ANSWER 具⇧ ASK YOUR TEACHER PRACTICE ANOTHER ill ASK YOUR TEACHER PRACTICE ANOTHER 3. [-/4 Points] DETAILS MY NOTES LARLINALG8 6.4.013. ASK YOUR TEACHER PRACTICE ANOTHERarrow_forward
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