Psychology 6140

- Interactive Rank Exercise
- Here you get to try out your understanding of the rank of a matrix online! Try several exercises at difficulty level 1, then try several at level 2. Highly recommended.
- Linear Transformations Applet
- Enter coefficients for a 2 × 2 matrix, and see the effect it has as a linear transformation.
- Linear transformations of points Another online linear transformation applet.
**imlproj.sas**- Projections: Projecting a vector in a vector space, and the Gram-Schmidt process, in excruciating detail!

ods listing; proc iml; %include iml(matlib); reset print log;which defines functions

For R, there is a similar collection of functions in the matlib package you can load into your R session.

library(matlib)

- Chap 3, Problem 7 -- part (a) only.
For this problem, try to follow G&C's approach or that in
the IML example imlproj.
You can create a matrix X containing all three vectors
(as columns) with the expression
X = t({ 1 2 3, 3 0 2, 3 1 1});

You can use the`gsorth`function to verify your results. - Chap 4, Problem 7. For this problem, you can use the
`R(X)`function to verify your answer, but use some other method to find the rank. - Chap 4, Problem 9b

* © 1995 Michael Friendly*