MAS 3105
AM: Jan 31, 2008
Quiz 2 and Key
Prof. S. Hudson
Note on problem 1: ‘Find
B
’ means  write out all 9 entries of
B
.
‘Check’ usually
means  show me the calculation on paper. For 1c and 1d, I’ll accept a short proof instead,
if you prefer. Parts 1a  1d are closely related, so do them in order, and you should not
need any trial and error. A transpose might help with one part.
1) [10pts each part] 1a) For the matrix
A
given below, check that
A
3
=
O
. Such a matrix
is called
nilpotent
.
A
=
0
1
0
0
0
1
0
0
0
1b) Find a nonzero 3x3 matrix
B
, so that
AB
=
O
(for the same
A
as above).
1c) Find two nonzero 3x3 matrices
C
and
D
so that
C

D
=
A
.
Then, check that
CB
=
DB
.
1d) Find nonzero 3x3 matrices
E
,
F
and
G
so that
EF
=
EG
. Check.
2) [20pts] Choose ONE of these to prove. Use words and sentences and standard methods
to completely explain your reasoning and your formulas. Some of these are just parts of
theorems we did in class. If so, you are NOT allowed to simply quote the theorem! You
ARE allowed to use previous theorems, definitions and/or previous HW.
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 Spring '09
 JULIANEDWARDS
 Matrices, Prof. S. Hudson, ﬁrst MATLAB problem, similar HW problems

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