Differential Equations with Boundary-Value Problems
9th Edition
ISBN: 9781337632515
Author: Dennis G. Zill
Publisher: Cengage Learning US
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Chapter 10.3, Problem 2E
To determine
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1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix
A.
= [{² 1]
A =
b) Verify that PT AP gives the correct diagonal form.
2
01
-2
3
2) Given the following matrices A =
-1
0
1] an
and B =
0
1
-3
2
find the following matrices:
a) (AB) b) (BA)T
3) Find the inverse of the following matrix A using Gauss-Jordan elimination or
adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I).
[1 1 1
A = 3 5 4
L3 6 5
4) Solve the following system of linear equations using any one of Cramer's Rule,
Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and
check the correctness of your answer.
4x-y-z=1
2x + 2y + 3z = 10
5x-2y-2z = -1
5) a) Describe the zero vector and the additive inverse of a vector in the vector
space, M3,3.
b) Determine if the following set S is a subspace of M3,3 with the standard
operations. Show all appropriate supporting work.
13) Let U = {j, k, l, m, n, o, p} be the universal set. Let V = {m, o,p), W = {l,o, k}, and X = {j,k). List the elements of
the following sets and the cardinal number of each set.
a) W° and n(W)
b) (VUW) and n((V U W)')
c) VUWUX and n(V U W UX)
d) vnWnX and n(V WnX)
9) Use the Venn Diagram given below to determine the number elements in each of the following sets.
a) n(A).
b) n(A° UBC).
U
B
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Chapter 10 Solutions
Differential Equations with Boundary-Value Problems
Ch. 10.1 - In Problems 16 write the given nonlinear...Ch. 10.1 - Prob. 2ECh. 10.1 - In Problems 16 write the given nonlinear...Ch. 10.1 - Prob. 4ECh. 10.1 - In Problems 16 write the given nonlinear...Ch. 10.1 - In Problems 16 write the given nonlinear...Ch. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Prob. 9ECh. 10.1 - Prob. 10E
Ch. 10.1 - Prob. 11ECh. 10.1 - Prob. 12ECh. 10.1 - Prob. 13ECh. 10.1 - Prob. 14ECh. 10.1 - Prob. 15ECh. 10.1 - In Problems 716 find all critical points of the...Ch. 10.1 - In Problems 2326 solve the given nonlinear plane...Ch. 10.1 - In Problems 2326 solve the given nonlinear plane...Ch. 10.1 - In Problems 2326 solve the given nonlinear plane...Ch. 10.1 - In Problems 2326 solve the given nonlinear plane...Ch. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECh. 10.1 - Prob. 29ECh. 10.1 - Prob. 30ECh. 10.2 - In Problems 916 classify the critical point (0, 0)...Ch. 10.2 - Prob. 10ECh. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - In Problems 916 classify the critical point (0, 0)...Ch. 10.2 - In Problems 916 classify the critical point (0, 0)...Ch. 10.2 - In Problems 916 classify the critical point (0, 0)...Ch. 10.2 - Prob. 16ECh. 10.2 - Prob. 17ECh. 10.2 - Determine a condition on the real constant so...Ch. 10.2 - Prob. 19ECh. 10.2 - Prob. 20ECh. 10.2 - Prob. 21ECh. 10.2 - Prob. 22ECh. 10.2 - Prob. 23ECh. 10.2 - In Problems 23-26 a nonhomogeneous linear system...Ch. 10.2 - Prob. 25ECh. 10.2 - Prob. 26ECh. 10.3 - Prob. 1ECh. 10.3 - Prob. 2ECh. 10.3 - Prob. 3ECh. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.3 - In Problems 310, without solving explicitly,...Ch. 10.3 - In Problems 310, without solving explicitly,...Ch. 10.3 - Prob. 8ECh. 10.3 - Prob. 9ECh. 10.3 - In Problems 310, without solving explicitly,...Ch. 10.3 - Prob. 11ECh. 10.3 - In Problems 1120 classify (if possible) each...Ch. 10.3 - Prob. 13ECh. 10.3 - Prob. 14ECh. 10.3 - Prob. 15ECh. 10.3 - Prob. 16ECh. 10.3 - Prob. 17ECh. 10.3 - Prob. 18ECh. 10.3 - Prob. 19ECh. 10.3 - Prob. 20ECh. 10.3 - Prob. 21ECh. 10.3 - Prob. 22ECh. 10.3 - Prob. 23ECh. 10.3 - Prob. 24ECh. 10.3 - Prob. 25ECh. 10.3 - Prob. 26ECh. 10.3 - Prob. 27ECh. 10.3 - Show that the dynamical system x = x + xy y = 1 y...Ch. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Prob. 31ECh. 10.3 - Prob. 32ECh. 10.3 - Prob. 33ECh. 10.3 - Prob. 34ECh. 10.3 - Prob. 35ECh. 10.3 - Prob. 36ECh. 10.3 - When a nonlinear capacitor is present in an...Ch. 10.3 - Prob. 38ECh. 10.3 - Prob. 39ECh. 10.4 - Prob. 1ECh. 10.4 - Prob. 2ECh. 10.4 - Prob. 3ECh. 10.4 - Prob. 4ECh. 10.4 - Prob. 5ECh. 10.4 - Prob. 6ECh. 10.4 - Prob. 7ECh. 10.4 - Prob. 8ECh. 10.4 - Prob. 9ECh. 10.4 - Competition Models A competitive interaction is...Ch. 10.4 - Prob. 12ECh. 10.4 - Prob. 13ECh. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Additional Mathematical Models Damped Pendulum If...Ch. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - Prob. 20ECh. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10 - Prob. 1RECh. 10 - Prob. 2RECh. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Prob. 7RECh. 10 - Prob. 8RECh. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Discuss the geometric nature of the solutions to...Ch. 10 - Classify the critical point (0, 0) of the given...Ch. 10 - Prob. 14RECh. 10 - Prob. 15RECh. 10 - Prob. 16RECh. 10 - Prob. 17RECh. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Prob. 20RE
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- 10) Find n(K) given that n(T) = 7,n(KT) = 5,n(KUT) = 13.arrow_forward7) Use the Venn Diagram below to determine the sets A, B, and U. A = B = U = Blue Orange white Yellow Black Pink Purple green Grey brown Uarrow_forward8. For x>_1, the continuous function g is decreasing and positive. A portion of the graph of g is shown above. For n>_1, the nth term of the series summation from n=1 to infinity a_n is defined by a_n=g(n). If intergral 1 to infinity g(x)dx converges to 8, which of the following could be true? A) summation n=1 to infinity a_n = 6. B) summation n=1 to infinity a_n =8. C) summation n=1 to infinity a_n = 10. D) summation n=1 to infinity a_n diverges.arrow_forward
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