Assignment2Solutions - MAT224 Assignment 2 SOLUTIONS Due...

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MAT224 Assignment 2 - SOLUTIONSDue Tuesday Oct 13 at the beginning of the lecture1.In each part, a linear map (also called a linear transformation) between two vector spaces is given, to-gether with a basisαof the domain and a basisβof the target. Find[T]βα, referred to as the matrix ofTwith respect to basesαandβ.(a)V=Span{sin2x,cos2x}C(R),Tthe identity map onV(i.e.T:VVgiven byT(v) =vforallvV),α={sin2x,cos2x}andβ={1,cos(2x)}. (You may want to look at Question 2(e) onAssignment 1.)Let us evaluateTon the vectors ofαand write the resulting vectors as linear combinations ofvectors inβin order to find the columns of the matrix[T]βα.

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