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Prove the following T is linear in the following definitions (a) T : R3 ?R2 is defined...

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Advance Math

Prove the following T is linear in the followingdefinitions
(a) T : R3 ?R2 is defined by T(x,y,z) = (x?y,2z)
(b) T : R2 ?R3 is defined by T(x,y) = (x?y,0,2x+y)
(c) T : P2(R) ? P3(R) is defined by T(f(x)) = xf(x)+f(x)

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