MATH 1302  PRACTICE SECOND MIDTERM EXAM SOLUTIONS
WINTER 2008
1. Let
A
=
•
3 7

1
0 4

8
‚
,
B
=
1
2
1
/
2

8
0
0
3
2
/
3
5
,
C
=
2
0
1

1
3
4
,
D
=
•
2 8

4
0 3
4
‚
a) Which of the following operations are deﬁned?
AB, BA, AC, CA, AD, DA
For those that are deﬁned, what is the size of the resulting matrix?
Answer:
BA
,
AD
and
DA
are not deﬁned because the sizes do not match.
AB
is deﬁned
and is a 2
×
3 matrix.
AC
is deﬁned and is a 2
×
2 matrix.
CA
is deﬁned and is a 3
×
3
matrix.
b) Which of the following operations are deﬁned?
A
+
B, A
+
D, A
+
D
+
B,
2
A

D
For those that are deﬁned, what is the result?
Answer:
A
+
B
and
A
+
D
+
B
are not deﬁned. The other operations are deﬁned and
A
+
D
=
•
5 15

5
0
7

4
‚
,
2
A

D
=
•
4 6
2
0 5

20
‚
c) What are
A
T
and
B
T
?
Answer:
A
T
=
3
0
7
4

1

8
,
B
T
=
1

8
3
2
0
2
/
3
1
/
2
0
5
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MAT 1302  PRACTICE SECOND MIDTERM EXAM SOLUTIONS
2. a) Suppose
A
is a 6
×
8 matrix and the product
AB
T
is deﬁned and is a 6
×
10 matrix.
What is the size of
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 Fall '09
 MarianKupczynski
 Math, Linear Algebra, Invertible matrix, Midterm Exam Solutions

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