Math 20F
First Midterm
January 27, 2003
•
PRINT NAME
•
Write version on your blue book and
VERSION A
hand in this exam inside your blue book.
•
There are a total of 40 points possible.
•
No BOOKS, NOTES or CALCULATORS are allowed.
•
You must show your work to receive credit.
1. (4 pts.) Fill in the following blanks.
(a) If
A
is an
n
×
n
matrix and there is a matrix
B
such that
, we call
B
the
inverse of
A
.
(b) If
A
and
B
are matrices such that
a
ij
=
b
ji
for all
i
and
j
, we call
B
.
2. (15 pts.) Let
A
=
1
0

1
0
0
0
0
1
1
1
0

1
2
2
0
3
.
(a) How many solutions does
A
x
= (1 0 0 0)
T
have? Justify your answer.
(b) How many solutions does
A
x
= (0 0 0 1)
T
have? Justify your answer.
(c) Either find a
b
so that
A
x
=
b
has exactly one solution or explain why this is
impossible.
3. (10 pts.) Prove or give a counterexample:
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 Spring '03
 BUSS
 Math, Determinant, Matrices, Diagonal matrix, blue book

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