Question: QUESTION 1 (10 MARKS) (a) Let V be R2, and the set of all ordered pairs (x, y) of real numbers. Define an addition by

QUESTION 1 (10 MARKS) (a) Let V be R2, and the set of all ordered pairs (x, y) of real numbers. Define an addition by (a, b) + (c, d) = (ac, [b - d[) for all (a, b) and (c, d) in V. Define a scalar multiplication by k . (a, b) = (a, kb) for all k E R and (a, b) in V. Verify the following axioms: (i) utv =v+u (2.5m) (ii) (k + m)u = ku + mu (2.5m) (b) Let V be R2 with the standard definitions of addition and scalar multiplication. Let W = lla - 2b . where a, b E R) be a subset of V. Determine whether W is a subspace of V. (5m)

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