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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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Topic review (newest first)

Ricky
2006-02-10 12:39:02

I'm going to change your scalars to k and l, since n is normally used to signify the length of a vector.

Since you don't know the dimension the vector is in, you have to use infinite sequence notation:

In R^n:

a = <a0, a1, .... an>

Then:

k(la) = k(<la0, la1, .... lan>) = <kla0, kla1, ... klan>

But

l(ka) = l(<ka0, ka1, ... kan>) = <kla0, kla1, ... klan>

And are thus, equal.

NoSash
2006-02-10 09:53:22

How can I prove the associative law (multiplication) using vectors:
m(na) = (mn)a    where m and n are real numbers, and a is a vector?

There are three cases to prove:
m>0, n>0
m<0, n<0
m>0, n<0 and m<0, n>0


I have no idea where to start.

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