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Linear Algebra : Linear transformations, Diagaonalization and Adjoints

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Let V be a , but with the weighted inner product, ,
,where and . Let be the linear transformation given by T(a,b,c)=(3a-2c,b,3a+10c).

a. Show that T can be diagonalized and find a basis for V comprised of eigenvectors of T.
b. Find the matrix of the adjoint of T with respect to the basis .

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(a) Since , then the matrix representation of , ...

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