Dear class:

Since we do not have enough class time,
I am further amanding the teaching plan.
The final exam will cover the following
sections:
5.2, 5.3, 6.1, 6.3 (up to p347).

The exam problems will be similar to the 
homework problems. 

Below is a list of study guide.
Please pay extra attention on basic problems
like how to compute ... of a matrix and
how to fit a set of data?

Given a matrix A, how to find the basis
for N(A), R(A), N(A^T), R(A^T), etc?

Given a subspace S, how to find a basis
for the orthogonal complement of S?

How to determine whether a linear
system of equation Ax=b has a solution?

How to get the least square solution of a 
overdetermined linear system of equation Ax=b? 

What exactly does the "least square solution" mean?

When is the "least square solution" unique?

How to fit a set of data using linear and
quadratic polynomials using least square solution?

What is the orthogonal projection operator onto R(A)?

How to compute the eigenvalues and eigenvectors
of a matrix A?

Given a diagonlizable matrix A, how to find a matrix X 
such that X^{-1}AX is diagonal?  What is the meaning of X?

How is the eigenvalues related to the trace
and determinant of a matrix?

How to compute the powers and inverse of a 
diagonalizable matrix?

What is a stochastic matrix? what can you say
about the eigenvalue of a stochastic matrix?

The homeworks are:
5.2: 1,2,3,4,6,7,8,9,13
5.3: 1,2,3,5,6
6.1: 1(e,f,g,k),3,4,6,11,12,13,21,23
6.1: 1(a,b,d) ,2(a,b,d) ,3(a,b,d)
     4, 6, 9, 17, 18, 20.