FIRST COURSE IN DIFF.EQ.-WEBASSIGN
11th Edition
ISBN: 9781337652476
Author: ZILL
Publisher: CENGAGE L
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Textbook Question
Chapter 8.2, Problem 22E
In Problems 21–30 find the general solution of the given system.
22.
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(Nondiagonal Jordan form) Consider a linear system with a Jordan form that
is non-diagonal.
(a) Prove Proposition 6.3 by showing that if the system contains a real eigenvalue
入
=
O with a nontrivial Jordan block, then there exists an initial condition with a
solution that grows in time.
(b) Extend this argument to the case of complex eigenvalues with Reλ = 0 by
using the block Jordan form
Ji
=
0
W
0
0
3000
1
0
0
1
0
ω
31
0
You manage a chemical company with 2 warehouses. The following quantities of
Important Chemical A have arrived from an international supplier at 3 different
ports:
Chemical Available (L)
Port 1
400
Port 2
110
Port 3
100
The following amounts of Important Chemical A are required at your warehouses:
Warehouse 1
Warehouse 2
Chemical Required (L)
380
230
The cost in£to ship 1L of chemical from each port to each warehouse is as follows:
Warehouse 1 Warehouse 2
Port 1
£10
Port 2
£20
Port 3
£13
£45
£28
£11
(a) You want to know how to send these shipments as cheaply as possible. For-
mulate this as a linear program (you do not need to formulate it in standard
inequality form) indicating what each variable represents.
(b) Suppose now that all is as in the previous question but that only 320L of
Important Chemical A are now required at Warehouse 1. Any excess chemical
can be transported to either Warehouse 1 or 2 for storage, in which case the
company must pay only the relevant transportation…
Suppose we have a linear program in standard equation form
maximize cx
subject to Ax = b,
x > 0.
and suppose u, v, and w are all optimal solutions to this linear program.
(a) Prove that z = u+v+w is an optimal solution.
(b) If you try to adapt your proof from part (a) to prove that that u+v+w
is an optimal solution, say exactly which part(s) of the proof go wrong.
(c) If you try to adapt your proof from part (a) to prove that u+v-w is an
optimal solution, say exactly which part(s) of the proof go wrong.
Chapter 8 Solutions
FIRST COURSE IN DIFF.EQ.-WEBASSIGN
Ch. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - Prob. 6ECh. 8.1 - In Problems 710 write the given linear system...Ch. 8.1 - In Problems 710 write the given linear system...Ch. 8.1 - In Problems 16 write the given linear system in...Ch. 8.1 - Prob. 10E
Ch. 8.1 - In Problems 1116 verify that the vector X is a...Ch. 8.1 - Prob. 12ECh. 8.1 - In Problems 1116 verify that the vector X is a...Ch. 8.1 - In Problems 1116 verify that the vector X is a...Ch. 8.1 - In Problems 1116 verify that the vector X is a...Ch. 8.1 - In Problems 1116 verify that the vector X is a...Ch. 8.1 - In Problems 1720 the given vectors are solutions...Ch. 8.1 - In Problems 1720 the given vectors are solutions...Ch. 8.1 - In Problems 1720 the given vectors are solutions...Ch. 8.1 - In Problems 1720 the given vectors are solutions...Ch. 8.1 - In Problems 2124 verify that the vector Xp is a...Ch. 8.1 - In Problems 2124 verify that the vector Xp is a...Ch. 8.1 - In Problems 2124 verify that the vector Xp is a...Ch. 8.1 - In Problems 2124 verify that the vector Xp is a...Ch. 8.1 - Prove that the general solution of the homogeneous...Ch. 8.1 - Prove that the general solution of the...Ch. 8.2 - In Problems 112 find the general solution of the...Ch. 8.2 - In Problems 112 find the general solution of the...Ch. 8.2 - In Problems 112 find the general solution of the...Ch. 8.2 - Prob. 4ECh. 8.2 - In Problems 112 find the general solution of the...Ch. 8.2 - In Problems 112 find the general solution of the...Ch. 8.2 - Distinct Real Eigenvalues In Problems 112 find the...Ch. 8.2 - Distinct Real Eigenvalues In Problems 112 find the...Ch. 8.2 - Prob. 9ECh. 8.2 - Prob. 10ECh. 8.2 - Distinct Real Eigenvalues In Problems 112 find the...Ch. 8.2 - Distinct Real Eigenvalues In Problems 1-12 find...Ch. 8.2 - In Problems 13 and 14 solve the given...Ch. 8.2 - In Problems 13 and 14 solve the given...Ch. 8.2 - In Problem 27 of Exercises 4.9 you were asked to...Ch. 8.2 - (a) Use computer software to obtain the phase...Ch. 8.2 - Find phase portraits for the systems in Problems 2...Ch. 8.2 - In Problems 2130 find the general solution of the...Ch. 8.2 - In Problems 2130 find the general solution of the...Ch. 8.2 - In Problems 2130 find the general solution of the...Ch. 8.2 - Prob. 24ECh. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - In Problems 2130 find the general solution of the...Ch. 8.2 - In Problems 2130 find the general solution of the...Ch. 8.2 - In Problems 2130 find the general solution of the...Ch. 8.2 - In problem 2130 find the general solution of the...Ch. 8.2 - In problem 3132 solve the given initial-value...Ch. 8.2 - Prob. 32ECh. 8.2 - Show that the 5 5 matrix...Ch. 8.2 - Prob. 34ECh. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - In Problems 35 46 find the general solution of the...Ch. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - Prob. 42ECh. 8.2 - Prob. 43ECh. 8.2 - Prob. 44ECh. 8.2 - Prob. 45ECh. 8.2 - In Problems 3546 find the general solution of the...Ch. 8.2 - In Problems 47 and 48 solve the given...Ch. 8.2 - In Problems 47 and 48 solve the given...Ch. 8.2 - Prob. 49ECh. 8.2 - Prob. 50ECh. 8.2 - 38. dxdt=4x+5ydydt=2x+6y 39. X = (4554)X 40. X =...Ch. 8.2 - Prob. 53ECh. 8.2 - Show that the 5 5 matrix...Ch. 8.2 - Prob. 55ECh. 8.2 - Examine your phase portraits in Problem 51. Under...Ch. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - Prob. 2ECh. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - Prob. 6ECh. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - In Problems 18 use the method of undetermined...Ch. 8.3 - In Problems 9 and 10, solve the given...Ch. 8.3 - Prob. 10ECh. 8.3 - Prob. 11ECh. 8.3 - (a) The system of differential equations for the...Ch. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 14ECh. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 16ECh. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 19ECh. 8.3 - Prob. 20ECh. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 22ECh. 8.3 - Prob. 23ECh. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 26ECh. 8.3 - Prob. 27ECh. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 31ECh. 8.3 - In Problems 1332 use variation of parameters to...Ch. 8.3 - Prob. 33ECh. 8.3 - In Problems 33 and 34 use (14) to solve the given...Ch. 8.3 - The system of differential equations for the...Ch. 8.3 - Prob. 36ECh. 8.4 - In problem 1 and 2 use (3) to compute eAt and...Ch. 8.4 - Prob. 2ECh. 8.4 - Prob. 3ECh. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.4 - Prob. 6ECh. 8.4 - Prob. 7ECh. 8.4 - Prob. 8ECh. 8.4 - In problem 912 use (5) to find the general...Ch. 8.4 - Prob. 10ECh. 8.4 - Prob. 11ECh. 8.4 - Prob. 12ECh. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - In problem 1518 use the method of Example 2 to...Ch. 8.4 - In problem 1518 use the method of Example 2 to...Ch. 8.4 - In problem 1518 use the method of Example 2 to...Ch. 8.4 - Prob. 18ECh. 8.4 - Let P denote a matrix whose columns are...Ch. 8.4 - Prob. 20ECh. 8.4 - Prob. 21ECh. 8.4 - Prob. 22ECh. 8.4 - Prob. 23ECh. 8.4 - Prob. 24ECh. 8.4 - Prob. 25ECh. 8.4 - A matrix A is said to be nilpotent if there exists...Ch. 8 - fill in the blanks. 1. The vector X=k(45) is a...Ch. 8 - fill in the blanks. The vector...Ch. 8 - Consider the linear system X=(466132143)X. Without...Ch. 8 - Consider the linear system X = AX of two...Ch. 8 - In Problems 514 solve the given linear system. 5....Ch. 8 - In Problems 514 solve the given linear system. 6....Ch. 8 - In Problems 514 solve the given linear system. 7....Ch. 8 - In Problems 514 solve the given linear system. 8....Ch. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - In Problems 514 solve the given linear system. 11....Ch. 8 - Prob. 12RECh. 8 - Prob. 13RECh. 8 - Prob. 14RECh. 8 - (a) Consider the linear system X = AX of three...Ch. 8 - Prob. 16RE
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