Are x² + x + 2, x² - 3x + 1, and 5x² - 7x + 7 linearly dependent?

[Naeem]

Q. { x^2 + x + 2 , x^2 -3x + 1, 5x^2 -7x + 7 }

Prove wether or not the above function's are linearly dependent.

Any help shall be very helpful!

 

[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.