Need Both parts to the homeowrk. Im not sure how to exactlyprove this. I know th

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Need Both parts to the homeowrk. Im not sure how to exactlyprove this. I know that i need to prove that W is non-empty, closed under scalar multiplication, and closed under addition.

Prove that W is a subspace of V

MATH 307 Homework 8 Let V = R4. Let W = {w E R4 : (1,2,3,4). w =0}. Prove that W is a subspace of V. Let T: Rn left arrow Rn be a linear transformation. Let W ={x E Rn : T(x) = 5x}. Determine whether or not W is a subspace of if, and specifically determine whether each of the three axioms holds or does not hold.

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