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 = S1 AS . In this case S1 AS is [ 2 1 1 1 ][ 5 241 ][ 111 2 ] = [ 2 1 1 1 ][ 313 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 ﬁnd, the method here is easy....
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 Fall '08
 lee
 Linear Algebra, Scalar, scalars c1, Bretscher

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