1. Find the solution to the following system of equations by row reducing the augmented matrix, and check your answer.

2. Find the elementary matrices corresponding to the first six elementary row operations you used in 1. above, and then multiply them together as follows to find the matrix F:

Name _______________________             Linear Algebra, Quiz 1, Summer 2004               Page 2

3. Find the six inverses of the six elementary matrices you found in 2. above, and multiply these together in such a way that you get the inverse of F. Check that you found the inverse of F by multiply your answer times the matrix F.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

4. [Extra Credit] This is a continuation of 2. above. Find all the remaining elementary matrices corresponding to the rest of the elementary row operations that you used in 1. Use these together with those found in 2. to compute the matrix inverse of A, and check that it is the inverse of A. Note that your answer must be correct to receive this extra credit.