Math205/Linear Algebra I Test Study Guide

----Test # 2-----

Second Test:Friday, November 13, 1998

....General Information About The Exam....

....(this information is the same as it was for Test #1)....

....(check the test #1 test guide page for details )....

A FEW IMPORTANT REMINDERS!

The test will be worth 80 points and will 
constitute roughly 25% of the total number of test points
for the course.

You will have 1hr and 20min to work on the test.

All of your work must be placed in the "Blue Book(s)"
that will be provided for you.

The answers in the Blue Book(s) must appear in the same order
as they appear on the test sheet, and so you will need to
plan ahead and leave necessary space if you intend to
work the problems out of order.

    

....Specific Information About The Exam....

0. All assigned homework problems (section 2.1-3.3 old book)
                                  (section 2.1-3.4 new book (skip 3.3))          

1. Be able to describe each of the three types of elementary matrices
   and their inverves 

2. Be able to prove that the inverse of AB is  
   B-inverse times A-inverse

3. Be able to prove that the inverse of A-transpose is the 
   transpose of A-inverse
   
4. Be able to explain why given a square matrix A, which can be row
   reduced without swaps, then A = LU, where L is lower triangular
   ,invertible, with ones on the diagonal and U is upper
   triangular
   
5. Be able to explain why AX=B has a solution if and only if LY=B
   and UX=Y (and why LY=B is always solvable) (using 4)  

6. Be able to give a detailed definition of a Vector Space

7. Define a subspace of a vector space (2 ways)

8. Define the four fundamental subspaces associated with
   a matrix A
 
9. Be able to prove N(A) is a subspace of Rn and and R(A)
   is a subspace of Rm
      
10.Be able to Prove that every solution of AX=B is of the 
   form X=Xp+Xn, where Xp is a particular solution of AX=B 
   and Xn lies in N(A).

(last updated 6:05PM on 11-4-98)