 
Summary: Mathematics 3C, Fall 2011
Worksheet 4, TA Grace Kennedy
NAME:
MY WEBSITE: http://math.ucsb.edu/kgracekennedy/Fall2011 3C.html
Course Website: Access through GauchoSpace.
Write clearly and justify every step as if this were an exam.
1. Consider the system of linear equations:
x  y + z = 0
x + 2y  3z = 0
3x  y  z = 0
(a) Find a basis for the null space of the coefficient matrix.
(b) What does the null space represent?
(c) Is the set of solutions to this system a vector space?
2. Consider the set of solutions to the system of linear equations on the green
midterm:
Solution Set =
r
