 
Summary: Mathematics 3C
Linear Algebra Review Questions
Fall 2011, Kennedy
NAME:
Website: http://math.ucsb.edu/kgracekennedy/Fall2011 3C.html
Course Website: Access through GauchoSpace.
Use clear presentation and justify every step.
1. Do the set of 2x2 matrices with trace equal to 1 form a vector space? If not, explain why. If so find a
basis.
S = {A M2×2(R)trace(A) = 1}
Could this problem be altered to produce a different result? If so, rewrite the new problem and find a
solution.
2. Find a basis for the following vector spaces and state their dimension:
(a) S = Span{
1
2
,
1
1
,
