Let U, V, and W be the following subspaces of \(\mathbb{R}^3\):
\(U = \{(x, y, z) \mid x = z\}\),
\(V = \{(x, y, z) \mid x = y = 0\}\),
\(W = \{(x, y, z) \mid x + y + z = 0\}\).
Verify that \(U + V = \mathbb{R}^3\), \(U + W = \mathbb{R}^3\) and \(V + W = \mathbb{R}^3\). In any of the cases, is
the sum direct?