ASSIGNMENT 2
MATH 270, WINTER 2010.
DUE: 5PM, FEBRUARY 9, 2010.
Assignments must have your name, student number, course number and TA’s name on the
first page. Please submit them by placing them in the box marked “Assignments” outside the
Maths Office (Burnside Hall, 10th floor). Show all working and justifications!
(1)
(a) Use Gaussian elimination to invert the matrix
U
=
1
3
1

2

2

2
1

2

2

2
1
and thereby compute all powers
U
n
of
U
.
[
6 marks
]
(b) Substitute
U
into the Maclaurin series expansion of cos
x
to show that cos
U
is a mul
tiple of the identity matrix.
[
4 marks
]
[
Total: 10 marks
]
(2) Define the
degree
of a polynomial
p
(
x
)
to be the maximal power of
x
appearing.
For
example,
x
2
+
3
x
+
2 has degree 2 whereas the constant polynomial 5 has degree 0. Funnily
enough, the degree of the zero polynomial is taken to be

∞
.
(a) Is the set of all polynomials of degree 6 a vector space?
[
1 mark
]
(b) Is the set of all polynomials of degree less than 6 a vector space?
[
1 mark
]
(c) How about the set of all polynomials of degree greater than 6?
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '10
 Ridout
 Math, Linear Algebra, Vector Space, Complex number

Click to edit the document details