Consider the linear transformationT:R3R2 given byT(x,y,z)=(3x4y+z,2xz)and be={(2,1,0),(1,0,3),(4,3.2)},={(1,3,2),(0,1,2),(1,1,1)}{(1,3),(2,4)}={(2,5),(4,1)}ordered bases.

(a1) Find the matrices of coordinate changesQ=[I]P=[I]

(a2) Corroborates that[T]=P1[T]Q

(b) Calculates the dual bases of and .

(c) GivenTt the transpose function of T, verify that[Tt]=([T])t

This is the original exercise:

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