Let Dg = { x, y | x2=1, y3=1, xyx = y} consider the map p: D3 → GL₂ (A) defined by p (y) = P(-(i) p (x) = 1 cos 2/3 -sin 2/3 sin 2/3 cos 2/3 Check that p is a representation. (i) (ii) Find the character of p.

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A: “Since you have posted multiple questions, we will provide the solution only to the first question…

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Q: Graph of f

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A: Let

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A: Here's a summary of the answers:  Solutions:(a) Find the range of γ (b) Use the definition to show…

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Q: mplify ƒ (x, y, z, w) to the simplest form. The Karnaugh map can b

A: Answer:   f(x, y, z, w) = y'w' + yz'w

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Q: The transformation T: R? - R', T|a b=[a - 8a). -a is linear ulgn O Ind.

A: See solution below

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