Summary: Mathematics 3C, Fall 2011
Worksheet 4, TA Grace Kennedy
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
Solution Set =