Show that the following sets with the given operations fail to be vector spaces by identifying all
Question:
(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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Related Book For
Elementary Linear Algebra with Applications
ISBN: 978-0471669593
9th edition
Authors: Howard Anton, Chris Rorres
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