Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 76E
Related questions
Question
17
![In Exercises 11-14, find the value(s) of h for
are linearly dependent. Justify each answer.
11.
13.
15.
- 17.
3
-5
HAD
7
19.
5
12
h
5
-9
7
UND AND
6
3
8
2
3
Determine by inspection whether the vectors in Exercises 15-20
are linearly independent. Justify each answer.
[][][][]
5
h
-9
5
0
[3]
0
12.
14.
27
-6
h
7
-4
HOD
-3
4
16. -2
[+][-
6
20.
-3
9
18.
• AN
-27
5
408
3
In Exercises 21 and 22, mark each statement True or False. Justify
each answer on the basis of a careful reading of the text.
21. a. The columns of a matrix A are linearly independent if the
equation Ax = 0 has the trivial solution.
b.
If S is a linearly dependent set, then each vector is a linear
combination of the other vectors in S.
c.
The columns of any 4 x 5 matrix are linearly dependent.
d. If x and y are linearly independent, and if {x,y,z) is
linearly dependent, then z is in Span {x,y).
22. /a. Two vectors are linearly dependent if and only if they lie
on a line through the origin.
b. If a set contains fewer vectors than there are entries in the
vectors, then the set is linearly independent.
c. If x and y are linearly independ
28. Ho
col
29. Co
the
30. a.
b.
Exercise
operation
31. Give
is the
of A
32. Give
35.
plus
a nor
Each state
or false (f
example t
example is
is true, giv
why a stat
here than i
33. If v₁..
is line
34. If V₁.
linear](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff5a5d7bf-20ae-45d2-981f-6a6741ca8eb9%2F628db3c8-9af1-4978-8890-923da1fa5512%2Ffn6hdz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In Exercises 11-14, find the value(s) of h for
are linearly dependent. Justify each answer.
11.
13.
15.
- 17.
3
-5
HAD
7
19.
5
12
h
5
-9
7
UND AND
6
3
8
2
3
Determine by inspection whether the vectors in Exercises 15-20
are linearly independent. Justify each answer.
[][][][]
5
h
-9
5
0
[3]
0
12.
14.
27
-6
h
7
-4
HOD
-3
4
16. -2
[+][-
6
20.
-3
9
18.
• AN
-27
5
408
3
In Exercises 21 and 22, mark each statement True or False. Justify
each answer on the basis of a careful reading of the text.
21. a. The columns of a matrix A are linearly independent if the
equation Ax = 0 has the trivial solution.
b.
If S is a linearly dependent set, then each vector is a linear
combination of the other vectors in S.
c.
The columns of any 4 x 5 matrix are linearly dependent.
d. If x and y are linearly independent, and if {x,y,z) is
linearly dependent, then z is in Span {x,y).
22. /a. Two vectors are linearly dependent if and only if they lie
on a line through the origin.
b. If a set contains fewer vectors than there are entries in the
vectors, then the set is linearly independent.
c. If x and y are linearly independ
28. Ho
col
29. Co
the
30. a.
b.
Exercise
operation
31. Give
is the
of A
32. Give
35.
plus
a nor
Each state
or false (f
example t
example is
is true, giv
why a stat
here than i
33. If v₁..
is line
34. If V₁.
linear
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