tut01 - THE UNIVERSITY OF SYDNEY PURE MATHEMATICS Linear...

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Unformatted text preview: THE UNIVERSITY OF SYDNEY PURE MATHEMATICS Linear Mathematics 2012 Tutorial 1 1. a ) Calculate the matrix product 3 0 4 1 1 2- 1 3 5 5- 2 4 . b ) Hence find the solution to the system of linear equations that corresponds to the augmented matrix 3 0 4 31 1 1 2 11- 1 3 5 9 . 2. Each of the following matrices is the reduced row echelon form of an augmented matrix be- longing to a system of linear equations in the variables x i , ( i = 1 , 2 , . . . ) . (Both the systems represented here have infinitely many solutions – why?) For each augmented matrix (i) determine the number of parameters needed to solve the system and (ii) express the solution of the system in parametric form. a ) parenleftBigg 1 4 1- 5- 1 parenrightBigg b ) parenleftBigg 1 2 6 1 5 1- 1 parenrightBigg 3. Recall that R 3 = braceleftBigparenleftBig x 1 x 2 x 3 parenrightBigvextendsingle vextendsingle vextendsingle x 1 , x 2 , x 3 ∈ R bracerightBig is a vector space. Describe each of the followingis a vector space....
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This note was uploaded on 02/06/2012 for the course MATH 2061 taught by Professor Notsure during the Three '09 term at University of Sydney.

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tut01 - THE UNIVERSITY OF SYDNEY PURE MATHEMATICS Linear...

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