MATH 201

Checklist  for  Test 1,   September 24,  2007

The test will cover primarily Chapter 2. Section 3.1 will not be covered. 
Note: understanding the content of Chapter 1 is also important, even though 
the problems will generally address topics from that chapter only indirectly. 


1.      Basic matrix operations. You need to know how to add, multiply etc. 
vectors and matrices. Just as importantly, you need to be able to explain 
why given operation can not be performed (for example, multiplying a  2 x 2 
matrix by a vector of height 4). 

2. 	Properties of matrix operations. You may be asked to determine 
whether two expressions involving matrices are equal, or to simplify an 
expression. Important issues here are: what is the inverse of a product 
of two (or more) matrices? what is the transpose of a product? what is 
the transpose of the transpose? what happens if you apply an operation 
to a special matrix (such as symmetric, diagonal or permutation).   

3.      Gaussian elimination (this is the heart of the test). You need to 
know how to find the LU, LDU or LPU decompositions of a matrix, the inverse 
of a matrix, or to solve a system of equations using row operations. 
You need to know how to use the decomposition A=LU to simply solve the 
system Ax=b (where x and b are vectors), or how to use the inverse of A 
to solve that system.  In some cases you may be asked to choose a method.