Find, if possible, a one to one linear transformation T R 3 R 4 and an onto linear transformation S R 4 R 3 such that the composition W R 3 R 3 where W(x) S(T(x)) is neither one to one nor onto

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Question: Find, if possible, a one-to-one linear transformation T : R 3 R 4 and an onto linear transformation S : R 4 R 3 such

Find, if possible, a one-to-one linear transformation T : R³ R⁴ and an onto linear transformation S : R⁴ R³ such that the composition W : R³ R³ where W(x) = S(T(x)) is neither one-to-one nor onto.

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