Andrew D. Lewis
2014
MATH 307
Homework # 6
Date Due:
2014/02/28
3.4-1 Solution: Suppose that we have vectors v1 , . . . , vk 2 V with one of them
zero. Without loss of generality (by relabelling, if necessary), suppose that
v1 = 0. Then
1 v1 + 0 v2 + + 0
Andrew D. Lewis
2014
MATH 307
Homework # 12
Date Due:
2014/04/16
P1. For the following R-linear maps, compute their eigenvalues, eigenvectors, generalised eigenvectors, and the algebraic and geometric multiplicities of all eigenvalues. Determine whether t
Andrew D. Lewis
2014
MATH 307
Homework # 11
Date Due:
2014/04/09
4.5-1(b,d) Solution: (b) We have
P ( ) = det
1
1
0
1
)2 .
= (1
Thus we have a single eigenvalue = 1 with algebraic multiplicity 2.
Eigenvectors for the eigenvalue 1 are solutions of the line
Andrew D. Lewis
2014
MATH 307
Homework # 13
Date Due:
2014/04/23
P1. In class we used the following pairs of adjectives to characterise ordinary
dierential equations:
1. scalar/vector;
2. nonlinear/linear;
3. (variable coecient)/(constant coecient);
4. in
Andrew D. Lewis
2014
MATH 307
Homework # 4
Date Due:
2014/02/12
2.5-1(b,d) Solution: (b) The determinant of the matrix is zero, so it has no
(d)
inverse.
The determinant of the matrix is 4, and so it has an inverse.
2.5-2(b,d) Solution: Note that we have
Andrew D. Lewis
2014
MATH 307
Extra Credit Assignment
Date Due:
2014/05/22
Rationale
In this course you have learned to perform many tedious operations that, if
you think about it for a second, are obviously best left to a computer since
they can clearly