MAST10007 Computer Lab 4
Its all about the definitions!
One of the keys to doing well at Linear Algebra (and many other
maths and stats subjects) is understanding the terminology used
in the course.
Often words in everyday use are given precise mathematic
MAST10007 Computer Lab 3
This week the lab exercises are designed to help you understand
the geometric meaning of determinants as areas of parallelograms and volumes of parallelepipeds (the higher dimensional
versions).
This is important for integration i
function [A] = rrefmod2(A)
%REFMOD2
Reduced row echelon form using modulo 2 rithmetic.
%
R = RREFMOD2(A) produces the reduced row echelon form of A.
%
%
See also RREF, RREFMOVIE, RANK, ORTH, NULL, QR, SVD.
[m,n] = size(A);
% Find the initial matrix modulo
MAST10007 Computer Lab 7
Help! I cant read your message!
Hamming Codes - An Application of Vector Spaces
Corruption of data is a major problem in digital storage
and transmission.
One way of correcting corrupted bits of data is to add
some redundancy in
MAST10007 Computer Lab 8
Linear Transformations/Computer Graphics
Today you will be exploring the basic linear transformations in R2.
Linear transformations show up again and again in mathematics,
statistics, engineering, physics and so forth.
For example
function plot2dd(X)% plot2d Two dimensional plot.% X is a matrix with 2 rows
and any number of columns.% plot2d(X) plots these columns as points in the plane
% and connects them, in order, with lines.% The scale is set to [-20, 20] in
both directions.% Fo
function
ppped1(A,E);%Takes the rows of A and E draws parallelepipeds spanned
by %thesez=[0;0;0];a1=A(1,:)';a2=A(2,:)';a3=A(3,:)';x=a1+a2;y=a1+a3;y2=a2+a3;
B=[z a1 x a2 z];C=[a3 a3 a3 a3 a3];D=B+C;
plot3(B(1,:),B(2,:),B(3,:),'b','LineWidth',2)hold on
plot
MAST10007 Computer Lab 2
This week the lab exercises give you the opportunity to further understand the theory and techniques in Linear Algebra especially
systems of equations and
matrix inverses.
Recall from class that you use Gaussian elimination to f
MAST10007 Computer Lab 6
1 + 1 6= 2!
A New Vector Space
Today you will be introduced to the vector space Fn
2.
In the context of this vector space you will revise many of the
concepts and definitions that you saw for Rn.
Try to remember the definitions wi
function eigsvdshow(arg)
%eigsvdshow Graphical demonstration of eigenvalues and singular values.
%
%
This is the same MATLAB's eigshow utility, except that more information
%
is displayed on the screen.
%
%
eigsvdshow presents a graphical experiment showi
MAST10007 Computer Lab 10
Eigenthings
Last week you discovered that, given a linear transformation, using a basis that gives a diagonal matrix of transformation is a
great idea for understanding the geometry of the transformation.
If T : Rn Rn is a linear
function varargout = linspan(varargin)
% LAB3 M-file for Lab3.fig
%
LAB3, by itself, creates a new LAB3 or raises the existing
%
singleton*.
%
%
H = LAB3 returns the handle to a new LAB3 or the handle to
%
the existing singleton*.
%
%
LAB3('CALLBACK',hObj
function [handle] = drawvec(v,color,s);
% DRAWVEC(v,color,s) graphs the vector v using
% the color specified by the second input
% argument. If no second argument is specified
% the default color is red. The initial point
% of the plot is the origin. An a
function eigsvdshow(arg)
%eigsvdshow Graphical demonstration of eigenvalues and singular values.
%
%
This is the same MATLAB's eigshow utility, except that more information
%
is displayed on the screen.
%
%
eigsvdshow presents a graphical experiment showi
function varargout = linspan(varargin)
% LINSPAN M-file for linspan.fig
%
LINSPAN, by itself, creates a new LINSPAN or raises the existing
%
singleton*.
%
%
H = LINSPAN returns the handle to a new LINSPAN or the handle to
%
the existing singleton*.
%
%
LI
MAST10007 Computer Lab 5
More Definitions!
Today you will be revisiting the concept of span. But this week it
will be done in the context of running, understanding and editing
the contents of short programs that produce graphics.
We remind you of the defi