Suppose v = span( v) c r". show that there are vectors w1 , . , wk e v that are mutually orthogonal (i. e., wi wi =0 whenever i j) that also span v. (hint: let w1 = v1. using techniques of section 2, define w2 so that span(w, w2) = span (v1, v2) and wi w2 = 0. continue.)

David estimated he had about 20 fish in his pond. a year later, there were about 1.5 times as many fish. the year after that, the number of fish increased by a factor of 1.5 again. the number of fish is modeled by f(x)=20(1.5)^x. create a question you could ask that could be answered only by graphing or using a logarithm.