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Problem 5: (2 points each) Show that the following transformations are linear. (a) $T:R_{3}→R_{2}$, where $T(x,y,z)=(x+z,−2y)$. (b) $T:R_{3}→R_{4}$, where $T(x,y,z)=(2x−z,y+z,0,x−3y)$. (c) $T:P_{2}→P_{3}$, where $T[p(x)]=xp(x)$. Problem 6: (2 points each) Show that the following transformations are not linear. (a) $T(x,y,z)=(x−y,y+z_{2})$. (b) $T(x,y,z)=(x−y,y+z,1+z)$

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