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[–] 0 points 4 points (+4|-0) ago  (edited ago)

Nah, anything you write is vacuously correct. You can even write "false," and that would be a correct answer.

The only way to get this wrong is to not answer.

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[–] 0 points 1 points (+1|-0) ago

How do you answer 12? I scraped through college algebra sr yr and this shit is way over my head..

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[–] 0 points 1 points (+1|-0) ago

Let n = dim V, since it is finite dimensional. Because v=/=0, there is a base of V given by u_1=v,u_2,...,u_n. Since it is a base, each vector w in V has a unique expression as a linear combination as the elements of the base. Therefore it is possible to define P:V-->k as follows: given w in V, w=av+bu_2+...+cu_n, so P(w)=a. Clearly, P(v)=P(1v)=1, so only have to check that P is linear.

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[–] [S] 0 points 0 points (+0|-0) ago  (edited ago)

Wave a magic wand.

This is linear algebra, so from college algebra it goes:

College Algebra -> Pre-Calc and Trigonometry -> Calc 1 -> Calc 2 -> Calc 3 and/or Calc 4 -> Differential Equations -> Linear Algebra.

My highest "math" course I've completed is Differential Equations so I don't think I can quiet explain this in simpler terms.

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[–] 0 points 0 points (+0|-0) ago

Ah math. The hole that just gets deeper. Cheers OP

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[–] 0 points 0 points (+0|-0) ago

As a guy with a philosophy degree, 14 neatly summarizes... pretty much everything I read and every time I went to class.

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[–] [S] 0 points 0 points (+0|-0) ago

Sorry to hear that.