MATH221 December 2008
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• Q1 (a) • Q1 (b) • Q2 (a) • Q2 (b) • Q3 (a) • Q3 (b) • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q7 (a) • Q7 (b) • Q8 (a) • Q8 (b) • Q9 (a) • Q9 (b) • Q10 (a) • Q10 (b) •
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Let denote the standard basis for . We determined in part (a) that the matrix of T relative to the basis was
and we want to determine , the matrix of T relative to the basis .
We can begin by writing
Let The above equality gives us a relation (check this!) for the coordinates of a vector with respect to each basis (recall that if , where , then the coordinates of with respect to the basis B is ).
Now, we have by definition, and .
Therefore, we can write
and so multiplying by , we find , from which we conclude that . To determine , we just need compute
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