assignment 8 math 2280
TRANSCRIPT
Math 2280 - Assignment 8
Dylan Zwick
Spring 2013
Section 5.4 - 1, 8, 15, 25, 33
Section 5.5 - 1, 7, 9, 18, 24
Section 5.6 - 1, 6, 10, 17, 19
1
Section 5.4 - Multiple Eigenvalue Solutions
5.4.1 - Find a general solution to the system of differential equations be‘ow.
The
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5.4.8 Find a general solution to the system of differential equations below.
/25 12 Ox’=f —18 —5 0 )x
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5.4.25 - Find a general solution to the system of differential equations below. The eigenvalues of the matrix are given.
/ —2 17 4 \x’= f —1 6 1 ) x; A = 2.2.2.
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5.4.33 - The characteristic equation of the coefficient matrix A of the system
3 —4 1 043010 0 3 40043
is
= (A2 — 6.X + 25)2 = 0.
Therefore, A has the repeated complex conjugate pair 3+ 4i of eigenvalues. First show that the complex vectors
1 0i 010 10 i
form a length 2 chain {vi. v2} associated with the eigenvalue A =
3 — 4i. Then calculate the real and imaginary parts of the complex-valued solutions
v1e and (vitfv9)eAt
to find four independent real-valued solutions of x’ = Ax.
‘Note in the textbook there’s a typo in this vector.
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4
Matrix Exponentials and Linear Systems
5.5.1 - Find a fundamental matrix for the system below, and then find asolution satisfying the given initial conditions.
2 ix’1 9)x. x(O)=(32).
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More room for Problem 5.5.24, if you need it.
21
Nonhomogeneous Linear Systems
5.6.1 - Apply the method of undetermined coefficients to find a particularsolution to the system below.
= x + 2y + 3= 2x + y — 2
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22
More room for Problem 5.6.1, if you need it.
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More room for Problem 5.6.19, if you need it.
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31