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it 's not linearly.

Why?

if it was linearly, that should be w-v=v-u. ok??

I don't understand it.. Can you explain?

w-v=((0-0),(0-1),(1-2))=(0,-1,-1)
v-u=((0-1),(1-2),(2-3))=(-1,-1,-1) ok??

Can you calculate this?
\(\left|\begin{matrix}
1&2&3\\
0&1&2\\
0&0&1
\end{matrix}\right|\)

But why did you put the vector horizontally (row vector?!) but not vertically (column vector?!)

Hm, that is not actually right.

Please, write what \(n\) in \(\Re ^n\) ?

Not quite. [0, 0, 0] is too trivial...Hmmm... :\

But don't take a concrete vector \(\vec x\), like (1,2,3). Solve it in general.

:O Thanks!!!
As you may observe, I'm not quite clear with the concepts, right?