Linear Independence Check
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by Doreen De Leon
| 2 Questions
Note from the author:
A quick quiz on linear independence.
1
1
Is the set of vectors {(1, 2), (2, 4), (-3, 5)} linearly independent? Why or why not?
Yes, because the only way a(1,2)+b(2,4)+c(-3,5) = (0,0) is if a = b = 0.
Yes, because there are infinitely many solutions to the equation a(1,2)+b(2,4)+c(-3,5) = (0,0).
No, because the only way a(1,2)+b(2,4)+c(-3,5) = (0,0) is if a = b = 0.
No, because there are infinitely many solutions to the equation a(1,2)+b(2,4)+c(-3,5) = (0,0).
2
1
Given a set of n functions on an interval I whose Wronskian is W(x), how do we determine if the functions are linearly independent on I?
If W(x)=0 for all x in I, then the functions are linearly independent.
If W(x) is not zero for any x in I, then the functions are linearly independent.
If W(x) is not zero for at least one x in I, then the functions are linearly independent.
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