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. v E 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. v E v T
Solution Summary: The author explains that the outer product of mathbfv( mathrmE
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.
v
E
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.
Please draw a graph that represents the system of equations f(x) = x2 + 2x + 2 and g(x) = –x2 + 2x + 4?
Given the following system of equations and its graph below, what can be determined about the slopes and y-intercepts of the system of equations?
7
y
6
5
4
3
2
-6-5-4-3-2-1
1+
-2
1 2 3 4 5 6
x + 2y = 8
2x + 4y = 12
The slopes are different, and the y-intercepts are different.
The slopes are different, and the y-intercepts are the same.
The slopes are the same, and the y-intercepts are different.
O The slopes are the same, and the y-intercepts are the same.
Choose the function to match the graph.
-2-
0
-7
-8
-9
--10-
|--11-
-12-
f(x) = log x + 5
f(x) = log x - 5
f(x) = log (x+5)
f(x) = log (x-5)
9
10
11
12
13 14
Chapter 1 Solutions
Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
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