# MATH280 : ALGEBRA CHAPTER 3 ```ALGEBRA CHAPTER 3
LINEAR SPACES
MATH2011/2014
OUTCOMES
At the end of this chapter, every student must
MATH2011/2014
(1)
understand and be able to define the concepts of :
linear space, basis, dimension, independence, rank, eigenvalues and eigenvectors,
diagonalization, trace and the Cayley-Hamilton theorem.
(2)
know how to :

determine whether or not a given set forms a linear space;

find a basis and the dimension of a linear space;

determine whether or not given vectors or functions are independent;

ascertain the rank of a matrix

find eigenvalues and their corresponding eigenvectors;

to diagonalize a matrix;

apply diagonalization to solve simultaneous linear differential equations in order
to determine trajectories;

apply the Cayley-Hamilton theorem;

work through and understand related problems in prescribed literature;

apply the above techniques to problem solving in related engineering courses.
A D Love
January 2007
Alg3-Outcomes
```