Math 205 Matrix Worksheet
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1MATH 205: Quiz 4
Name:
1. What are the three requirements for a subset H of a vector space V to be a subspace?
(a)
(b)
(c)
2. Find a basis of the Nul(A) and Col(A).
1
2
5
3 6
1 0 0 1 1
2
2
1
0 3
0 1 0 1 0
A =
and rref (A) =
3
1
1 4 2
0 0 1 0 1
3. Write True or False. If false, give a counterexample.
(a) A spanning set is always a basis.
(b) A basis is always a spanning set.
(c) For
, any set of three vectors is a basis.
1
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