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 MS . In this case that is [ 3 5 1 2 ][ 3 411 ][ 251 3 ] = [ 3 5 1 2 ][ 231 2 ] = [ 1 1 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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This note was uploaded on 02/06/2011 for the course MATH 33a taught by Professor Lee during the Fall '08 term at UCLA.
 Fall '08
 lee
 Scalar

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