 
Summary: Math 320, "spring" 2011
before the first midterm
Typical Exam Problems
1. Consider the linear system of equations
2x1 + 3x2  2x3 + x4 = y1
x1 + 3x2  2x3 + 2x4 = y2
x1 + 2x3  x4 = y3
where x1, · · · , x4 are the unknowns, and y1, y2, y3 are given constants.
(i) If you want to find the general solution to this system by row reduction, then
which matrix do you have to rowreduce?
(ii) Compute the Reduced Row Echelon Form of the matrix you found in (i).
(iii) What is the general solution to the system of equations?
(iv) Answer the same questions for the system
2x1 + 3x2  2x3 + x4 = y1
x1 + 3x2  2x3 + 2x4 = y2
2x1 + 2x3  x4 = y3
2. A system of two equations with four unknowns has been rowreduced to the
matrix
1 0 0 1 4
0 1 2 3 1
