Linear Transformations Worksheet

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Linear Transformations Worksheet

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Linear Transformations Worksheet

1 8 Introduction to Linear Transformations Another way to view Ax b Matrix A is an object acting on x by multiplication to produce anewvectorAx or b EXAMPLE 2 4 3 6 1 2 2 3 8 12 4 2 4 3 6 1 2 2 1 0 0 0 Suppose A is m n SolvingAx b amounts to finding all in Rn which are transformed into vector b in Rm through multiplication by A multiply by A transformation Solution We do i and ii simultaneously Not linear due 1 Linear the matrix is 2 0 0 3 0 4 0 1 5 0 0 0 c Linear the matrix is 1 1 1 d Linear the matrix is 0 2 2 0

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