Let R2 have the inner product of Example 1 . Show that the Cauchy-Schwarz inequality holds for x=(3,−2) and y=(−2,1). [Suggestion: Study ∣⟨x,y⟩∣ 2.] EXAMPLE 1 Fix any two positive numbers-say, 4 and 5 -and for vectors u=(u 1 ,u 2 ) and v=(v 1 ,v 2 ) in R 2 , set ⟨u,v⟩=4u 1 v1+5u 2v2