The matrices and vectors listed in Eq. (3) are used in several of the exercises that follow. A = 3 1 4 7 2 6 , B = 1 2 1 7 4 3 6 0 1 C = 2 1 4 0 6 1 3 5 2 4 2 0 , D = 2 1 1 4 E = 3 6 2 3 , F = 1 1 1 1 u = 1 - 1 , v = - 3 3 (3) If x and y are vectors in R n , then the product x T y is often called an inner product. Similarly, the product x y T is often called an outer product. Exercises 35-40 concern outer products; the matrices and vectors are given in Eq. (3). In Exercises 35-40, form the outer products. ( A u ) A v T
The matrices and vectors listed in Eq. (3) are used in several of the exercises that follow. A = 3 1 4 7 2 6 , B = 1 2 1 7 4 3 6 0 1 C = 2 1 4 0 6 1 3 5 2 4 2 0 , D = 2 1 1 4 E = 3 6 2 3 , F = 1 1 1 1 u = 1 - 1 , v = - 3 3 (3) If x and y are vectors in R n , then the product x T y is often called an inner product. Similarly, the product x y T is often called an outer product. Exercises 35-40 concern outer products; the matrices and vectors are given in Eq. (3). In Exercises 35-40, form the outer products. ( A u ) A v T
Solution Summary: The author explains that the transpose of any matrix is found by changing the rows to columns and columns to rows.
The matrices and vectors listed in Eq. (3) are used in several of the exercises that follow.
A
=
3
1
4
7
2
6
,
B
=
1
2
1
7
4
3
6
0
1
C
=
2
1
4
0
6
1
3
5
2
4
2
0
,
D
=
2
1
1
4
E
=
3
6
2
3
,
F
=
1
1
1
1
u
=
1
-
1
,
v
=
-
3
3
(3)
If
x
and y are vectors in
R
n
, then the product
x
T
y
is often called an inner product. Similarly, the product
x
y
T
is often called an outer product. Exercises 35-40 concern outer products; the matrices and vectors are given in Eq. (3). In Exercises 35-40, form the outer products.
(
A
u
)
A
v
T
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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