Math 205A Quiz 08 page 1 March 21, 2008 NAME
1. Let A=
30 0
58−10
55 −7
.
1A. Find the characteristic polynomial of Ain factored form.
1B. One of the eigenvalues of Ais an odd number, the other is even. Find a basis for the eigenspace of
the odd one. Show all your work.
2. Let M=
1−1−355
211521
11110−1
−113−4−5
; then RREF([M|I4]) is
1040 2−20 1/2−5/2
0170−320 1/25/2
0001 0 10 0 1
0000 0 01−3/21/2
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))