Math 205a Quiz 08 - Bates College, 2008
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1Math 205A
Quiz 08 page 1
March 21, 2008
NAME
3 0
0
.
1. Let A =
5 8
10
5 5
7
1A. Find the characteristic polynomial of A in factored form.
1B. One of the eigenvalues of A is an odd number, the other is even. Find a basis for the eigenspace of
the odd one. Show all your work.
1
1
3
5
5
1 0 4 0
2
2 0
1/2
5/2
2
1
15
2
1
0 1 7 0
3
2 0
1/2
5/2
2. Let M =
; then RREF([M|I
]) is
4
1
1
11
0
1
0 0 0 1
0
1 0
0
1
1
1
3
4
5
0 0 0 0
0
0 1
3/2
1/2
Find bases for each of the following; use correct notation. You may write “same as” if appropriate; for
example, if the basis in (2G) were the same as for (2A) then “same as 2A” would be acceptable as the
answer to 2G.
2A. Col(M)
2B. Nul(M)
2C. Col(RREF(M))
2D. Nul(RREF(M))
2E. Row(M)
2F. Row(RREF(M))
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