Please solve part (d) specifically please in detail, will give rating. 1. Determine if the following maps T are linear. If so, find [T], the matrix of T. If not, give a specific counterexample to one of the properties of linearity. (a) T:R2?R2 given by T([x1?x2??])=[2x1?+33x2??8?] (b) T:R4?R3 given by T??x1?x2?x3?x4????=?x1??6x2??4x4?5x2??9x4?x4?

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Please solve part (d) specifically please in detail, will give rating.   1. Determine if the following maps T are linear. If so, find [T], the matrix of T. If not, give a specific counterexample to one of the properties of linearity. (a) T:R2?R2 given by T([x1?x2??])=[2x1?+33x2??8?] (b) T:R4?R3 given by T??x1?x2?x3?x4????=?x1??6x2??4x4?5x2??9x4?x4??? (c) T:R3?R given by T??x1?x2?x3????=[(x1?x2?x3?)1/3] (d) T:R2?R2 given by T([x1?x2??])=[ln(3x1?2x2?)tan(tan?1(7x1??9x2?))?] (e) Which of the nonlinear maps above satisfies T(cx)=cT(x) ? Show that T(cx)=cT(x) for this map T.

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