No knowledge of any specific computer program is needed for this course, but matlab is a particularly appropriate program for checking your work in this part of the course.
I don't want to lecture on use of matlab, but here are some very primitive instructions on getting started if you are in a Unix environment and on getting the row-reduced echelon form of a matrix. NONE OF THIS IS REQUIRED AND YOU ARE WELCOME TO USE ANY LINEAR ALGEBRA PROGRAM YOU WANT TO CHECK YOUR WORK. My comments are preceded by % signs.
% Type matlab
at the prompt ---
% you will see something like this:
zariski:hochster% matlab
To get started, type one of these: helpwin, helpdesk, or demo.
For product information, type tour or visit www.mathworks.com.
>>
% The >> is a prompt. You can feed in a matrix at
% the prompt by typing
>> A = [1 2 3; 4 5 6]
% The semi-colons ; separate rows.
% Spaces or commas can be used to separate entries of
% one row. If you type in the above (and hit Return) you
% will see this:
>> A = [1 2 3; 4 5 6]
A =
1 2 3
4 5
6
>>
% Now, if you want to get the reduced row echelon form of A
% type in rref(A) at the prompt (and hit Return):
>> rref(A)
ans =
1 0
-1
0 1
2
% An alternative is to name the answer for future manipulations
% yourself, e.g. type in B = rref(A) (and hit return)
>> B = rref(A)
B =
1 0
-1
0 1
2
>>
% The product of two matrices A,B can be entered as A*B,
% and the inverse of the square matrix A as inv(A).
% det(A) produces the determinant of the % square matrix A.
% norm(A) produces the length of the & row or column vector A.
% A' produces the transpose of the % matrix A, i.e. the same matrix but % with the rows and columns interchanged. % If A is 3 by 5 then A' is 5 by 3. % For example if A is
% 1 2 3 % 4 5 6
% then A' is
% 1 4 % 2 5 % 3 6
% The dot product of two vectors A and B % can be obtained by using transposes suitably % so that the first becomes a row and the second % a column, and then using * . E.g., for two % rows the dot product is A*B' while for % two columns the dot product is A'*B.
% null(A) produces a basis for the % kernel (also called the nullspace) % of A consisting of mutually % perpendicular (= orthogonal) vectors % of length 1. This means that what % is standardly produced will only be % correct to 4 decimal places and % fractions are typically introduced % even when that is not necessary.
% That's all for now.