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Unformatted text preview: ASSIGNMENT 3 for SECTION 001 Solutions Questions from the textbook Section 3-2: B1 [4 marks] ; B3 (a) and (b) [6 marks] ; B4 (b) and (c) [6 marks] ; and B5 [4 marks] In addition to the questions listed here, do the MATLAB question from Assignment 3 for the other sections; this may be found under Content > Assignments > Assignment 3 [2 marks] Other questions 1. [4 marks] The unit square in R 2 is parametrized by the formula r e 1 + s e 2 , r, s 1 , where e 1 and e 2 denote the columns of the 2 2 identity matrix. Let L be a linear transformation with standard matrix a b c d . Prove that the image of the unit square under L is a parallelogram of area | ad- bc | . The image of the unit square under L is L ( r e 1 + s e 2 ) = rL ( e 1 ) + sL ( e 2 ) , r, s 1 . This is the parametric formula of the parallelogram with sides L ( e 1 ) = a c and L ( e 2 ) = b d ; that is, with vertices (0 , 0), ( a, c ), ( b, d ) and ( a + b, c + d )....
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