136A6 - is a magic square with magic constant 34. (This...

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ASSIGNMENT 6 for SECTION 001 Questions from the textbook Section 4-3: B1 (a) and (c) [2 marks] , B2 [2 marks] , B5 [2 marks] and D2 [2 marks] Section 4-4: B2 [2 marks] , B3 [2 marks] , B5 [2 marks] , D4 (b) and (c) [2 marks] and D6 [2 marks] In addition to the questions listed here, do the MATLAB question from Assignment 6 for the other sections; this may be found under Content > Assignments > Assignment 6 [2 marks] Other questions 1. [6 marks] An n × n magic square is a matrix whose rows, columns and two main diagonals have entries adding up to the same number, the square’s magic constant . For example, the matrix 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1
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Unformatted text preview: is a magic square with magic constant 34. (This matrix appears in Durers Melencolia I .) Prove that the set of 3 3 magic squares is a vector space of dimension 3. 2. [4 marks] Given a polynomial p ( x ), let p ( i ) ( x ) denote its i th derivative. Let p ( x ) be a polynomial of degree n . Prove that B = p ( x ) , p (1) ( x ) , . . . , p ( n ) ( x ) is a basis for P n . Suppose p ( x ) = x n . Let S = x n , x n-1 , . . . , x, 1 denote the standard basis for P n . Find the change-of-coordinates matrices from B to S and from S to B ....
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This note was uploaded on 03/19/2009 for the course M m136 taught by Professor Fokshuen during the Spring '09 term at Waterloo.

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