Question: A function f : R - R is linear if: f ( x + ) ) = f(x)+f() f(kv) = kf(0) 1. Suppose that f

A function f : R" - R is linear if: f ( x + ) ) = f(x)+f() f(kv) = kf(0) 1. Suppose that f is linear. Show that Uf = (ve R" : f() = 0} is a subspace. 2. Use part (a) to show that: U(a1,...,an) = (x ER" : dixit ... anx, = 0) is a subspace of R" . 3. Find a basis for U(1,2,3) C R and calculate its dimension

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