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Unformatted text preview: k R then T ( r 1 v 1 + r 2 v 2 + + r k v k ) = r 1 T ( v 1 ) + r 2 T ( v 2 ) + + r k T ( v k ) . ii) T ( ) = where R n and R m . 4 theorem 1.4 If T : R n R m is a linear transformation, and B = { b 1 , b 2 , , b n } a basis for R n . Then: if v R n = T ( v ) is determined by T ( b 1 ) , T ( b 2 ) , , T ( b n ) . example 1.5 Suppose T : R 2 R 2 is a linear transformation and T ([1 , 1]) = [3 , 2] , T ([2 , 3]) = [7 , 7] . Find T ([ x, y ]) . 5 Homework: Suppose T : R 2 R 3 is a linear transformation and T ([1 , 2 , 1]) = [1 , 3 , 2] , T ([2 , 3 , 1]) = [2 , 2 , 7] , T ([1 , 1 , 2]). Find T ([ x, y, z ]). 6...
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This note was uploaded on 05/22/2010 for the course MATH MATA23 taught by Professor Sophie during the Spring '10 term at University of Toronto Toronto.
 Spring '10
 Sophie
 Linear Algebra, Algebra, Transformations

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