 
Summary: ANSWER KEY
REVIEW PROBLEMS FOR MIDTERM I
MATH2574H, SPRING 2012, UNIVERSITY OF MINNESOTA
GREG W. ANDERSON
This problem list is between 1.5 and 2 times the length of a typical exam. It is
a fair indication of questions you might see on the first midterm, but it is not an
absolutely complete review. For completeness you must make sure that you know
how to do all of the homework assigned in the course up to and including week 3.
Further note: Try to solve all the problems by hand, even those which give you
permission to use your calculator.
Problem 1
Solve the system of equations
2x y +5w = 1
2x +z +w = 3
using the standard method. Do your work entirely by hand.
Solution
The augmented matrix of the system is
2 1 0 5 1
2 0 1 1 3
We rowreduce all the way to reduced echelon form by the following steps:
