Posted by **mathstudent** on Saturday, June 9, 2007 at 11:56pm.

Let T1: P1 -> P2 be the linear transformation defined by:

T1(c0 + c1*x) = 2c0 - 3c1*x

Using the standard bases, B = {1, x} and B' = {1, x, x^2}, what is the transformation matrix

[T1]B',B

T(c0 + c1*x) = 2c0 - 3c1*x --->

T(1) = 2

T(x) = -3x

So, the matrix elements are:

T_{1,1} = 2

T_{1,2} = 0

T_{2,1} = 0

T_{2,2} = -3

T_{3,1} = 0

T_{3,2} = 0

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