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Linear Independence Check

Last updated over 7 years ago

2 questions

Note from the author:

A quick quiz on linear independence.

1

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Question 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).

Question 2

2.

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.