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
=
1
1
1
2
1
2
0

1
B
=
1

1
1
2
1
0
4

1
2
C
=
2
1
0
2
1

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

1
y
=
2

1
2
z
=

1

1
3
2
SOLUTION
A
z
=
5

5
B
y
=
5
3
13
C
v
=
3
2

1
6
C
x
=
1

2
3
4
D
v
=
1
1
D
x
=

1
1
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
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 Fall '08
 Gladue
 Calculus, Linear Algebra, Vectors, Matrices, Vector Space, ax, Linear map, linear transformation

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