Prove the following statement:

  • Thread starter Naeem
  • Start date
In summary, to prove the linearity of independence of the given functions, one can compute the wronskian and determine if it is equal to zero. If it is equal to zero, the functions are dependent, and if not, they are independent.
  • #1
Naeem
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0
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
 
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  • #2
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?
 
  • #3
My thought is to compute the wronskian:

and see if it is equal = 0 it is dependent, if not independent.
 
  • #4
That would be an excellent way to do it--- you would do well to recall the 3x3 determinant.
 

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Proving a statement means providing evidence or logical reasoning to demonstrate that the statement is true. This involves using mathematical or scientific methods to support the validity of the statement.

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A statement is considered valid if it follows logically from a set of premises or assumptions. In other words, if the statement is based on sound reasoning and can be supported by evidence, it is considered valid.

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