Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Consider the following false statement:
For all integers a and b, if ab = 1 (mod 8), then a = 1 (mod 8) or b = 1 (mod 8).
(a) Which of the following could be used as a counterexample. Select all that apply.
a = -7 and b = −7
a = 1 and b = 23
☐ a = 3 and b: = −5
☐ a = 4 and b = 6
□ a = −1 and b = −9
1. Given
X' =
X
3
e2t
(a) Verify that X₁(t) = (e) and X2(t) = (et)
-
are solutions to the given system.
(b) Verify that X₁(t) and X2(t) form a fundamental set on the interval (-∞, ∞).
(c) Write the general solution to the given system.
(d) Find the solution that satisfies the initial condition X(0) = ( 2 ).
Prove that a relation X defined on a set A that is reflexive, symmetric and antisymmetric is an equivalence relation and determine the equivalence classes.
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