MHB Determinant - Proof for distinct real numbers

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The discussion centers on proving a mathematical statement involving determinants and distinct real numbers. One participant successfully proved part (a) but seeks assistance with part (b), questioning whether a geometric interpretation exists. The potential relevance of the Vandermonde matrix is mentioned as a resource. Another participant suggests using the property of determinants, specifically that a determinant equals zero if its columns form a linear combination. The conversation highlights the need for further exploration of geometric interpretations in relation to determinants.
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I was able to prove a), but I am unsure how to prove b. Is there some sort of geometric interpretation I should be aware of?
 

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Rido12 said:
I was able to prove a), but I am unsure how to prove b. Is there some sort of geometric interpretation I should be aware of?

Hey Rido! ;)

One way is apply the property of a determinant that it is 0 iff its columns form a linear combination. (Thinking)
 

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