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Level 9

Vector Addition & Scalar Multiplication


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Axiom 1
u + v is a vector in Rn
Axiom 2
u + v = v+u
Axiom 3
(u + v) + w = u + (v + w)
Axiom 4
u + 0 = u
Axiom 5
u + (-u) = 0
Axiom 6
cu is a vector in Rn
Axiom 7
c(u + v) = cu + cv
Axiom 8
(c + d)u = cu + du
Axiom 9
c(du) = (cd)u
Axiom 10
1u = u