If w is a subspace of r n , show that w ∩ w⊥ = {0}. hint: start from definition, no complicated computation, it’s just some simple logic. note that if u · u = 0, then u must be a zero vector. also, both w and w⊥ are vector spaces, hence {0} ⊂ w ∩ w⊥ is clear, you just need to show another inclusion.

The graph and table shows the relationship between y, the number of words jean has typed for her essay and x, the number of minutes she has been typing on the computer. according to the line of best fit, about how many words will jean have typed when she completes 60 minutes of typing? 2,500 2,750 3,000 3,250