MA106 Linear Algebra
Assignment 1
January 2011
Answer the questions on your own paper. Write your own name in the top lefthand corner, and your supervisors name in the top right-hand corner. Solutions to
Problems 1,3,4,5 only must be handed in by 2.00 pm
MA106 Linear Algebra
Assignment 5
February 2011
Answer the questions on your own paper. Write your own name in the top lefthand corner, and your supervisors name in the top right-hand corner. Solutions
to Problems 1, 3 and 4 only must be handed in by 2.00
MA106 Linear Algebra
Assignment 6
February 2011
Answer the questions on your own paper. Write your own name in the top lefthand corner, and your supervisors name in the top right-hand corner. Solutions
to Problems 1, 3 and 4 only must be handed in by 2.00
MA106 Linear Algebra
Assignment 7
February 2011
Answer the questions on your own paper. Write your own name in the top lefthand corner, and your supervisors name in the top right-hand corner. Solutions to
Problems 1, 2, 4 and 5 only must be handed in by 2
MA106 Linear Algebra
Assignment 8
March 2011
Answer the questions on your own paper. Write your own name in the top lefthand corner, and your supervisors name in the top right-hand corner. Solutions
to Problems 2, 4 and 5 only must be handed in by 2.00 pm
MA106 Linear Algebra
Assignment 9
March 2011
Answer the questions on your own paper. Write your own name in the top lefthand corner, and your supervisors name in the top right-hand corner. Solutions to
Problems 1, 2, 3 and 5 only must be handed in by 2.00
MA106 Linear Algebra
Assignment 4
February 2011
Answer the questions on your own paper. Write your own name in the top lefthand corner, and your supervisors name in the top right-hand corner. Solutions to
Problems 2, 4, 5 and 6 only must be handed in by 2
MA106 Linear Algebra
Assignment 2
January 2011
Answer the questions on your own paper. Write your own name in the top lefthand corner, and your supervisors name in the top right-hand corner. Solutions to
Problems 1, 3, 4 and 6 only must be handed in by 2.
1
Number systems and elds
We introduce the number systems most commonly used in mathematics.
1. The natural numbers N = cfw_1, 2, 3, 4, . . ..
In N, addition is possible but not subtraction; e.g. 2
3 62 N.
2. The integers Z = cfw_. . . , 2, 1, 0, 1, 2, 3,
Theorem 10.3. Let A = (ij ) be an n n matrix. Then det(AT ) = det(A).
Proof. Let AT = (
ij )
where
= ji . Then
ij
det(AT ) =
X
sign( )
1 (1) 2 (2)
.
n (n)
2Sn
=
X
sign( )
(1)1 (2)2
.
(n)n .
2Sn
Now, by rearranging the terms in the elementary product, we h
this case, it might be easier (for some people) to work it out using the matrix
multiplication! We have
cos
sin
cos
sin
sin
cos
sin cos
cos cos + sin sin
cos sin + sin cos
=
sin cos cos sin
sin sin cos cos
cos(
) sin(
)
=
,
sin(
)
cos(
)
which is t
MA106 Linear Algebra
Assignment 3
January 2011
Answer the questions on your own paper. Write your own name in the top lefthand corner, and your supervisors name in the top right-hand corner. Solutions to
Problems 1, 2, 3 and 5 only must be handed in by 2.
MA 1060
THE UNIVERSITY OF WARWICK
FIRST YEAR EXAMINATION: JUNE 2010
LINEAR ALGEBRA
Time Allowed: 2 hours
Read carefully the instructions on the answer book and make sure that the particulars
required are entered on each answer book.
Calculators are not ne