Consider the solution space W of the homogeneous system of linear equations x + 2y − z = 0, 2x − y + 3z = 0. (a) Find a basis for the solution space W, the set of all solutions (x, y, z). (b) Show that W is a subspace of R 3 . (c) Let u = (2, 1, −1) and v = (1, 2, 0) be vectors in R 3 show that W is a subspace of V = span(u, v) and V is a subspace of R 3.

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