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2.7
Consider the following list of 4 matrices and 4 vectors. There are 16 diﬀerent pairs of matrices and
vectors. Say for which pairs the matrix–vector product is deﬁned, for which it isn’t, and compute it when
it is.
A
=
h
1
1
1
2
1
2
0

1
i
B
=
±
1

1
1
2
1
0
4

1
2
²
C
=
2
1
0
2
1

2
5
1
D
=
h
0
1
1
0
i
v
=
h
1
1
i
x
=
h
1

1
i
y
=
±
2

1
2
²
z
=

1

1
3
2
SOLUTION
A
z
=
±
5

5
²
B
y
=
5
3
13
C
v
=
3
2

1
6
C
x
=
1

2
3
4
D
v
=
±
1
1
²
D
x
=
±

1
1
²
2.9
Let
A
=
1
1
1
2
1
2
0

1
2
0
0

1
3

2
0
2
and
x
=

1

2
2
1
. Compute the third entry of
A
x
without computing the
whole vector
A
x
.
SOLUTION
Using Theorem 3,
(
A
x
)
3
=

1(2)

2(0) + 2(0) + 1(

1) =

3
.
2.11
Let
f
be a linear transformation from
IR
2
to
IR
2
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This note was uploaded on 10/03/2010 for the course MATH 380 taught by Professor Gladue during the Fall '08 term at Roger Williams.
 Fall '08
 Gladue
 Calculus, Vectors, Matrices

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