Unformatted text preview: For f ( x ) = x n , f ( x ) = nx n1 . (You may use the product rule for derivatives ( fg ) = f g + fg in your argument.) (3) Prove that the sum of the interior angles of any convex ngon equals ( n2)180 ◦ . (4) 1.4.7: Guess a formula for A n and prove it using induction. (5) Let A 1 ,A 2 ,...,A n be nonsingular m × m matrices. Prove that the product A 1 A 2 ··· A n is nonsingular and that ( A 1 ··· A n )1 = A1 n ··· A1 1 . (*) Bonus: Prove that the Principle of Mathematical Induction and the WellOrdering Principle (stated below) are logically equivalent. WellOrdering Principle: Every nonempty set of positive integers has a smallest element; i.e. for any nonempty set of natural numbers S , there exists an m ∈ S such that m ≤ s for all s ∈ S . 1...
View
Full Document
 Spring '11
 Math, Linear Algebra, Logic, Algebra, Mathematical Induction, Natural number, correct English sentences

Click to edit the document details