Math 205a Quiz 7 - Bates College, 2007
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1Math 205A
Quiz 7, page 1
November 16, 2007
NAME
0 1
4
1
2
3
1 0
3 0 4
5
0 0
0
0
0
0
0 1
4 0 0
2
4 0
12
9
34
25
0 0
0 1 2
5
1. Fact: The matrix A =
is row equivalent to
.
3 6
15
0
12
3
0 0
0 0 0
0
2 4
10
0
8
2
0 0
0 0 0
0
1A. Find each of the following:
i) The rank of A.
ii) The dimension of the null space of A.
iii) A basis for the column space of A.
iv) A basis for the row space of A.
2. Suppose B ∈ M
.
3×5
2A. What are the maximum and minimum possible dimensions for Nul(B)? MAX:
MIN:
2B. What are the maximum and minimum possible values for the rank of B? MAX:
MIN:
4 4
3. Let C =
5 8
3A. Find the characteristic polynomial of C.
3B. Find the eigenvalues of C using the answer to (3A).
3C. Find an eigenvector of C corresponfing to the larger of the two eigenvalues in (3B).
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