Question

Solve 4 questions of quiz. each of them gives 0.25 point

1. Show that the following sets of elements in R³ form subspaces. (a). The set of all (x, y, z) such that x − 2y + z = 0. (b). The set of all (x, y, z) such that x = 3z and y = z.

2. (a). Let U = {(x, y) ∈ R² : 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1} and W = {(x, y) ∈ R² : x 2 + y 2 ≤ 1}. Are these sets subspaces of R^2? (b). Find the sum U + W.

3. If U and W are subspaces of a vector space V, show that U + W is a subspace

4.Show that functions f(t) = t and g(t) = 1/t defined for t > 0 are linearly independent.

Answer 1