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    10 Axioms of vector spaces

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    if u and v are objects in V, then u+v is in V
    1
    u+v = v+u
    2
    u+(v+w) = (u+v)+w
    3
    There is an object 0 in V called a zero vector for V,
    Such that 0+u = u+0 = u
    4
    For each u in V, there is an object -u in V, called a negative of u, such that u+(-u) = (-u)+u = 0
    5
    If k is any scalar and u is any object in V, then ku is in V.
    6
    k(u+v) = ku + kv
    7
    (k+m)u = ku+mu
    8
    k(mu) = (km)(u)
    9
    1u = u
    10

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