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Unformatted text preview: is S [ x ] B = [ x ] E , and that you are looking for the matrix M such that M [ x ] B = [ T ( x )] B . Since A [ x ] E = [ T ( x )] E , substituting gets you AS [ x ] B = S [ T ( x )] B , and M = S-1 AS . In this case S-1 AS is [ 2 1 1 1 ][ 5 2-4-1 ][ 1-1-1 2 ] = [ 2 1 1 1 ][ 3-1-3 2 ] = [ 3 1 ] . You could also do this by the one of the other methods discussed in Bretscher, but, when the inverse of S is easy to nd, the method here is easy....
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- Fall '08