Answer to Question #27049 in Algebra for melly gos

Question

1)Let V= R3. Show that W is a subspace of V where W = {(a, b, 0): a, b ϵ R}, i.e. W is the xy plane consisting of those vectors whose third component is 0.

2)Let V= R3. Show that W is not a subspace of V where W = {(a, b, c): a, b, c ϵ Q}, i.e. W consists of those vectors whose components are rational numbers.

3)Determine whether the vectors v1 = (2, -1, 3), v2 = (4, 1, 2) and v3 = (8, -1, 8) span R3.

4)Use system of linear equations form and row echelon form to show that the vectors (2, -1, 4), (3, 6, 2) and (2, 10, -4) are linearly independent.