Are These Functions Linearly Independent?

[Naeem]

Q. Prove whether or not the following are linearly independent.

1. f1 (x) = sqrt (x) + 5

2. f2(x) = sqrt (x) + 5x

3. f3(x) = x-1

How do we prove these?

Can anyone help

 

[Hurkyl]

Please read the guidelines for posting homework help questions.

https://www.physicsforums.com/showthread.php?t=4825

You must have had a thought on this problem already -- surely you know, say, the definition, or a relevant theorem?

 

[Naeem]

My thought is to compute the wronskian:

and see if it is equal = 0 it is dependent, if not independent.

 

[Theelectricchild]

That would be an excellent way to do it--- you would do well to recall the 3x3 determinant.