Which of the following sets of vectors are linearly independent?A. (4,8,-5), (-9, -4,-6), (-13, -12, -1)● B. (1, -2, 4), (-8, 7, 0), (3, 6, 5)C. (-8, -2), (8,2)• D. (4, 8,-5), (-9, -4, -6), (-13, -1, -12 ), ( 4, 11, -13)E. (-3, 1, -2), (1, 7,-8)• F. (-1, 5), (9,-1)● G. (-6, 1, 1, -2), (1, 7, -4,-9)H. (4, 6), (0,0)

Answered: Which of the following sets of vectors…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Which of the following sets of vectors are linearly independent?
A. (4,8,-5), (-9, -4,-6), (-13, -12, -1)
● B. (1, -2, 4), (-8, 7, 0), (3, 6, 5)
C. (-8, -2), (8,2)
• D. (4, 8,-5), (-9, -4, -6), (-13, -1, -12 ), ( 4, 11, -13)
E. (-3, 1, -2), (1, 7,-8)
• F. (-1, 5), (9,-1)
● G. (-6, 1, 1, -2), (1, 7, -4,-9)
H. (4, 6), (0,0)

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A vector is a quantity that has both magnitude and direction. It can be also defined as the mathematical quantity which obeys the set of axioms. In general, vectors are represented as $A = (A_{1}, A_{2}, A_{3})$ , where $A_{1}, A_{2}, A_{3}$ are called the components of the vectors. In this problem, we have to find which of the given vectors are linearly independent.