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Linear Transformation Exercises

Linear Transformation Exercises

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(b) T : R2!R2, satisfying T 1 1 = 1 2 ;T 2 3 = 2 5 Solution: We need to nd T(~e 2) and T(~e 2). Given the information we have, this is easiest to do by writing ~e 1 and ~e 2 as linear combinations of ˆ 1 1 ; 2 3 ˙ We start with ~e 1. We solve 1 0 = c 1 1 1 + c 2 2 3 Setting up the system of equations as usual and solving yields c 1 = 3;c 2 ...

  Satisfying

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