1.
Find the dimensions of
A
6 × 3
·
B
3 × 1
.
A.
3 × 1
B.
3 × 3
C.
6 × 1
D.
6 × 3
Hint
2.
State whether the product of
A
3 × 4
and
B
3 × 4
is defined, and if it is defined, state the dimensions.
A.
defined, 4 × 3
B.
defined, 3 × 4
C.
defined, 9 × 16
D.
undefined
Hint
3.
Which of the following is true concerning matrix multiplication of three matrices
A
,
B
, and
C
?
A.
AB
=
BA
for all cases
B.
AB
=
BA
for no cases
C.
C
(
A
+
B
) =
CA
+
CB
D.
(
A
+
B
)
C
=
CA
+
CB
Hint
4.
Given that
and
use the fact that
to find
AB
+
AC
.
A.
B.
C.
D.
Hint
5.
Which of the following properties does not hold for matrices?
A.
right distributive property
B.
commutative property of multiplication
C.
associative property of multiplication
D.
left distributive property
Hint