Math 2270 – Spring 2009
Linear Algebra Stimulus Package
Objectives:
•Learn how to generate matrices of specified ranks, whether full or rank deficient. Least squares
problems (which we’re studying now) are referred to as having full column rank or being rank
deficient.
•Earn 10 points to supplement your in-class exam 2 score.
Review the MATLAB appendix in Leon’s text, available for viewing on the course website:
www.math.usu.edu/~howland/teach/index2270.php
In addition to trying the commands described, practice the following:
keep a diary
>>diary filename
...
>>diary off
writes everything that appears in the command window after diary filename until diary off
in the file named in filename.
BASIC DATA ELEMENTS
Transpose the row vector generated by x=2:6 using x’ to get a column vector.
GENERATING MATRICES
To obtain information on the built-in functions to generate matrices, type: help rand.
MATRIX ARITHMETIC
Pay special attention to the operators +,-,*,’, and backslash. In this exercise we learn how
to generate matrices of specified rank by taking outer products of vectors (such as x*y’) and
matrix outer products (such as X*Y’).
MATLAB FUNCTIONS
To understand how to generate integer entries type: help round. To determine the rank of a
matrix you generate, check out help rank.
Take Home Portion of Exam 2
due Apr. 15
MATLAB Exercise p.171 #2 Turn in the diary of your session and your written discussion.
Be sure to provide every explanation you are asked for, and answer every question posed in
complete sentences. In particular, you will need to explain why the outer product of vector
x∈Rmand vector y∈Rnwill be an m×nmatrix with rank 1. You will also need to consider
the relation (1) in part (d), and what it tells you about the rank of matrix outer products.
