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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
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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16. 15. BEID · 17. 19. -6 5 18. -000-0000 5 -8 27 -3 12 11 4 4 22. 22. /a. -2 20. -3 411 9 5 3 1.1 0 0 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
Transcribed Image Text:16. 15. BEID · 17. 19. -6 5 18. -000-0000 5 -8 27 -3 12 11 4 4 22. 22. /a. -2 20. -3 411 9 5 3 1.1 0 0 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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