Math 0250 Exam 2
March 20, 2000
F. Beatrous
Name:
1. Find the eigenpairs for the matrix
111
0 2 0
013
Solution:
1
1
1
2
0
det(A I ) = det 0
0
1
3
1
1
0
3
= (2 ) det
= ( 2)( 1)( 3).
Thus the eigenvalues are 1, 2, and 3.
For the eivenvalue = 1,
which row re
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Math 0250 Exam 1
October 9, 2000
F. Beatrous
Name:
1. Find all fourth roots of 16. Your answer should list each fourth root exactly once.
2. Look at the oscillation
f (t) = cos t + sin t.
(a) Find a complex number A such that f (t) is the real part of Aei
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e h f hq
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d I ct h
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Review Topics for Exam 2
March 9, 1998
Characteristic polynomials, eigenvalues, eigenvectors
Page 110 Number 7, 9, 20
Homogeneous systems, general solutions, initial value problems
Page 126 Number 1, 4, 9
Matrix solutions, fundamental matrix
Page 135 N
Review Topics for Exam 1
October 1, 2002
Complex Numbers, Cartesian and Polar Representation
Page 8 Number 1, 3
Complex Exponentials
Represent a function of the form a cos(t) + b sin(t) as the real part of a complex
exponential Aeit . Interpretation of
Math 0250 Exam 2
November 2, 2001
F. Beatrous
1. Find the eigenpairs for the matrix
Name:
1
3
.
1 1
2. A is a real 2 2 matrix with eigenpairs
1 + i,
1
i
and
1 i,
1
i
.
(a) Find the real form of the general solution to the system X = AX .
(b) Find the solu
Math 0250 Exam 2
March 20, 2000
F. Beatrous
Name:
1. Find the eigenpairs for the matrix
111
0 2 0
013
2. The real 2 2 matrix A has eigenpair
1 + 2i,
1
i
.
(a) Find the general solution to the system X = AX in real form. (If you cant nd
the real form, then
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