(Solution) - Let L be the linear transformation defined in Exercise 2 -(2025 Original AI-Free Solution)

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Let L be the linear transformation defined in Exercise 2, Section 6.3.
(a) Find the transition matrix P from S' to S.
(b) Find the transition matrix from S to S' and verify that it is P-l.
(c) Find the transition matrix Q from T' to T.
(d) Find the representation of L with respect to S' and T'.
(e) What is the dimension of range L?