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}.
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}.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Question
21 pl
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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.
d.
The columns of any 4 x 5 matrix are linearly dependent.
If x and y are linearly independent, and if {x, y, z) is
linearly dependent, then z is in Span {x,y}.
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 independent, and if z is in
Span {x, y), then {x, y, z) is linearly dependent.
d.
If a set in R" is linearly dependent, then the set contains
more vectors than there are entries in each vector.
matrix. Use the notation of Example 1 in Section 1.2.
In Exercises 23-26, describe the possible echelon forms of the
23. A is a 3 x 3 matrix with linearly independent columns.
3
3
E
O
e.
e
19
W
h
3.
3.
35
30
37
38
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