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Lecture

# linear transformations

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University of Toronto Scarborough

Mathematics

MATA23H3

Sophie Chrysostomou

Winter

Description

Linear Transformations Denition: A function T : R n R m is a linear transformation if for all v,u R n and for all r R, the following are satised: i) T(u + v) = T(u) + T(v) ii) T(rv) = rT(u) Denition: If T : R R m is a linear transformation.Then: n 1. R is the domain of T. 2. R m is the codomain of T. n 3. If W R then: the image of W under T is T[W] = {T(w) w W}. n n 4. the range of T is T[R ] = {T(v) v R } . 5. If W R , then the inverse image of W under T is T 1[W ] = {v R n T(v) W } 1 n m The set T [{0 }] = {v R T(v) = )} ( where 0 R ) is called the kernel of T. www.notesolution.com

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