Question: Show that the following sets with the given operations fail to be vector spaces by identifying all axioms that fail to hold. (a) The set

Show that the following sets with the given operations fail to be vector spaces by identifying all axioms that fail to hold.
(a) The set of all triples of real numbers with the standard vector addition but with scalar multiplication defined by k(x, y, z) = (k2x, k2y, k2z).
(b) The set of all triples of real numbers with addition defined by (x, y, z) + (u, v, w) = (z + w, y + v, x + u) and standard scalar multiplication.
(c) The set of all 2 × 2 invertible matrices with the standard matrix addition and scalar multiplication.

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a Only Axiom 8 fails to hold in this case Let k and m be scalars Then k mx y z k m 2 x k m 2 y k m 2 ... View full answer

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