136A6S - ASSIGNMENT 6 for SECTION 001 Solutions Questions...

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ASSIGNMENT 6 for SECTION 001 Solutions 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 is a magic square with magic constant 34. (This matrix appears in D¨urer’s Melencolia I .) Prove that the set of 3 × 3 magic squares is a vector space of dimension 3. Let V denote the set of 3 × 3 magic squares. We prove that it is a subspace of the vector space of 3 × 3 matrices. First, the 3 × 3 zero matrix is an element of V ; its magic constant is 0. Second, let
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