Are the Wronskians set up and compared in this linear independent check?

nysnacc
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Homework Statement


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Homework Equations



The Attempt at a Solution


I set up the Wronskian?? and compare them?
 
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nysnacc said:

Homework Statement


View attachment 107662

Homework Equations



The Attempt at a Solution


I set up the Wronskian?? and compare them?
You could evaluate the Wronskian of the three functions, or you could use the definition of linear independence.
 
What is the definition of linear independance?
 
Isn't there a definition of linear independence in your textbook?

Note that "independance" is not a word. Whoever wrote the problem doesn't seem to be aware of this.
 
But will Wronskian easier of definition of Linear independence is more formal?
 
Forum rules require that you show some effort. I don't see any effort, just question after question. And I see the question is worth 5 points. Is this a take-home test you are supposed to work yourself?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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