In each of the following, determine whether the indicated addition and scalar multiplication of ordered triples of real numbers yields a vector space. For those that are not vector spaces, determine which properties of a vector space fail to hold.
a) (x1, y1, z1) + (x2, y2, z2) = (x1 + x2, y1 + y2, z1 + z2), c(x, y, z) = (cx, y, cz)
b) (x1, y1, z1) + (x2, y2, z2) = (z1 + z2, y1 + y2, x1 +x2), c(x,y,z) = (cx, cy, cz)
c) (x1, y1, z1) + (x2, y2, z2) = (x1 + x2, y1 + y2, – 2 z1 + z2), c(x, y, z) = (cx, y, cz)
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