MHB Determinant - Proof for distinct real numbers

Dethrone
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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)
 
Thread 'How to define vector field?'

Thread 'How to define vector field?'

Hello! In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way: I think so: higher-order terms can be neglected because partial derivative of second power and higher are equal to 0. Is this true? And how to define vector field correctly for this case? (In the book I found nothing and my attempt was wrong...
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