Prove the following statement:

  • Thread starter Naeem
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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.
 

Related to Prove the following statement:

What does it mean to "prove a statement"?

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.

How do you approach proving a statement?

The first step in proving a statement is to clearly define the statement and any relevant terms or concepts. Then, you can use deductive reasoning, mathematical equations, or experimental data to support your argument and demonstrate the truth of the statement.

What makes a statement valid?

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.

What types of evidence can be used to prove a statement?

There are various types of evidence that can be used to prove a statement, including mathematical proofs, experimental data, statistical analysis, and logical arguments. The type of evidence used will depend on the specific statement being proved.

Can a statement ever be proven beyond a doubt?

It is generally accepted in science that no statement can be proven with absolute certainty. However, a statement can be supported by a significant amount of evidence and be considered highly probable or true within a certain margin of error.

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