Exercise 6.1.1 Let V denote the set of ordered triples (x, y, z) and define addition in V as in R³. For each of the following definitions of scalar multiplication, decide whether V is a vector space. a. a(x, y, z) = (ax, y, az) b. a(x, y, z) = (ax, 0, az) c. a(x, y, z) = (0, 0, 0) d. a(x, y, z) = (2ax, 2ay, 2az)

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