 
Summary: Math 310: Midterm 1
October 10, 2006
Name: ID number:
There are 5 questions worth a total of 100 points, plus one small bonus question
worth 10 points. Please justify all your statements, and write neatly so that we can
read and follow your answers. Continue your answers on the back of the pages. Also,
please turn off cell phones.
Question 1. (20 points) (i) Find a basis for the subspace
W := {(x1, x2, x3, x4) F4
: x1 = x2  3x3 = x3 + x4},
and prove that the elements you give do form a basis.
(ii) Suppose that U is another subspace of F4
such that U + W = F4
. What can you
say about dim U?
1 20pt
2 20pt
3 20pt
4 30pt
5 10pt
