Math 2270 - Practice Exam 2
University of Utah
Fall 2012
Name:
/•
This is a 50 minute exam. Please show all your work, as a worked
problem is required for full points, and partial credit may be rewarded for
some work in the right direction.
1
1. (15 Points) Subspaces
For the following subsets of IPI’ explain why they are or are not subspaces of :
Th
R
(a) The set of all linear combinations of two vectors v, w E W.
(b) The set of all vectors with first component equal to 2.
(c) The set of all vectors with first component equal to 0.
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2. (20 points) For the following matrix, determine the special solutions
for the nulispace, calculate the nulispace, and give its dimension.
A=(
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3. (20 points) Fow the following matrix, calculate the rank, determine
the dimension of the column space, and provide a basis for the col
umn space:
B
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4. (15 points) Calculate the dimension, and find a basis for, the vector
space given by:
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