The ten axioms for vector spaces
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| Axiom 01 | If u and v are objects in V, then u + v is in V
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| Axiom 02 | u + v = v + u
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| Axiom 03 | u + (v + w) = (u + v) + w
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| Axiom 04 | There is an object 0 in V, called a "zero vector" for V, such that 0 + u = u + 0 = u for all u in V
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| Axiom 05 | For each u in V, there is an object -u in V, called a "negative" of u, such that u + (-u) = (-u) + u = 0
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| Axiom 06 | If k is any scalar and u is any object in V, then ku is in V
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| Axiom 07 | k(u + v) = ku + kv
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| Axiom 08 | (k + m)u = ku + mu
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| Axiom 09 | k(mu) = (km)u
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| Axiom 10 | 1u = u
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Created by:
Ultric
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