Exercises 29–34 require knowledge of the sum and direct sum of subspaces, as defined in...

Exercises 29–34 require knowledge of the sum and direct sum of subspaces, as defined in the exercises of Section 1.3.

Let

Prove that W₁ and W₂ are subspaces of V, and find the dimensions of W₁, W₂, W₁ + W₂, and W₁ ∩ W₂.