The set of all x ɛR ( means: x belongs to R ) for which the vectors : [1, x, 0] , [ 0, x² , 1] ,[0, 1, ×] are linearly independent Select one: O 1. {xɛ R:X # 1} O 2. {xɛ R:X -1} O 3. {xɛ R:Xx = 0 } O 4. {x ɛR:X # 0 }

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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The set of all x ɛR(means: x belongs to R) for which the vectors :
[1, x, 0] , [ 0, x² , 1],[0, 1, x] are linearly independent
Select one:
O 1. {xɛ R:x # 1}
O 2. {xɛ R:x -1}
O 3. {xɛ R:x = 0 }
O 4. {x ɛR:x ± 0 }
Transcribed Image Text:The set of all x ɛR(means: x belongs to R) for which the vectors : [1, x, 0] , [ 0, x² , 1],[0, 1, x] are linearly independent Select one: O 1. {xɛ R:x # 1} O 2. {xɛ R:x -1} O 3. {xɛ R:x = 0 } O 4. {x ɛR:x ± 0 }
Which of the following sets of vectors in R3 are linearly independent :
1. {[ 1, 0, 0 ], [ 0, 1, 0], [ 1, 1, 0 ]}
2. {[ 1, 0, 0 ], [ 0, 1, 0], [ 0, 0, 1 ]}
3. {[ 0, 1, 0], [ 1, 0, 1], [ 1, 1, 0 ]}
4. {[ 0, 0, 1], [ 0, 1, 0], [ 0, 1, 1 ]}
Select one:
1 and 4
1 and 2
2 and 3
3 and 4
Transcribed Image Text:Which of the following sets of vectors in R3 are linearly independent : 1. {[ 1, 0, 0 ], [ 0, 1, 0], [ 1, 1, 0 ]} 2. {[ 1, 0, 0 ], [ 0, 1, 0], [ 0, 0, 1 ]} 3. {[ 0, 1, 0], [ 1, 0, 1], [ 1, 1, 0 ]} 4. {[ 0, 0, 1], [ 0, 1, 0], [ 0, 1, 1 ]} Select one: 1 and 4 1 and 2 2 and 3 3 and 4
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