asmt1 - McGill University Math 270-2010 Fall: Applied...

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McGill University Math 270-2010 Fall: Applied Linear Algebra Written Assignment 1: due on Monday, Oct. 4, 2010 1. Give (3 × 5) matrix: A = ± ± ± ± ± ± 1 - 2 0 1 - 1 2 - 4 1 0 - 1 3 - 6 1 1 0 ± ± ± ± ± ± . (a) Determine the dimension of the subspaces col ( A ) and row ( A ); (b) Find the basis for col ( A ) and the basis of row ( A ); (c) Find the nullspace of A and the nullity null ( A ). (d) Let b = (1 , 1 ,a ) T . Discuss the existence and uniqueness of the solutions for the system A x = b . Determine the rank of its augmented matrix A # and demonstrate that for what numbers a , the system (i) has unique solution exists; (ii) does not have solution; or (iii) has no- unique solution. In this case, give a set of linear independent solutions. 2. Calculate the following matrix multiplications: (1 , 2 , 3)(2 , 3 , 4) T =?; (1 , 2 , 3) T (2 , 3 , 4) =? 0 , 0 , 1 , 0 0 , 1 , 0 , 0 1 , 0 , 0 , 0 0 , 0 , 0 , 1 1 , 2 , 3 , 4 2 , 3 , 4 , 5 3 , 4 , 5 , 6 4 , 5 , 6 , 7 ; 1 , 0 , 0 , 0 0 , 1
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This note was uploaded on 11/22/2010 for the course MATH math 270 taught by Professor Xu during the Winter '07 term at McGill.

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asmt1 - McGill University Math 270-2010 Fall: Applied...

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