MATH 4063-5023
Homework Set 3
1. Let F be a eld with exactly two elements (it will be isomorphic to Z2 ) and let V be a 2-dimensional
vector space over F. How many vectors are there in V ? How many di
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MATH 4063-5023
Homework Set 4
1. Let P be the vector space of polynomials with indeterminant x.Which of the following mappings are
linear transformations from P to itself
(a) T : p xp
(b) T : p 2p
(c)
MATH 4063-5023
Homework Set 6
1. Determine if the following matrices A are diagonalizable. When A is diagonalizable, provide both the
matrix C diagonalizing A and its diagonal form D (so that D = C1 A
LECTURE 2
Subspaces and Linear Independence
Last time we dened the notion of a eld F as a generalization of the set of real numbers, and the notion of
a vector space over a eld F as a generalization o
LECTURE 1
Introduction
The rudiments of linear algebra are familar to every scientist who knows what a vector is and every software
engineer who knows what an array is. In Math 3013 (Linear Algebra) t
MATH 4063-5023
Homework Set 5
1. Find the
2 0
(a) 0 2
0 0
2
(b) 0
0
characteristic polynomials and minimal polynomials of the following matrices.
0
0
2
1
1
2
1
2
0
2. Find the eigenvalues of the fol
MATH 4063-5023
Homework Set 1
1. Let F be a eld, and let Fn denote the set of n-tuples of elements of F, with operations of scalar
multiplication and vector addition dened by
[
[
1; : : : ;
n]
1; : :
LECTURE 4
Elementary Operations and Matrices
In the last lecture we developed a procedure for simplying the set of generators for a given subspace of the
form
S = spanF (v1 , . . . , vk ) := cfw_1 v1