Please give me \"written\" crystal clear answers! I will rate your answers immed

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Please give me "written" crystal clear answers! I will rate your answers immediately,

In each of the following, a function from one real vector space to another is given. Decide if the function is linear. If it is. explain briefly why- This will usually mean either doing calculations or writing something like. "We know any function of this form is linear. If it is not, give one example showing, why linearity fails. Please note: There is a bit of the jargon to practice getting right here. If L : V rightarrow U satishe? L v + v = alpha L v + L v, we say L preserves addition; if L alpha v = alpha Lv . we say L preserves multiply-.atim by scalars. Don't confuse these with closure under addition and multiplication by scalars. which are some what related but apply to checking whether you have a vector space, not checking whether a function is linear.

Explanation / Answer

a)

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