Did I get this right? I am trying to prove that the set T satisfies Properties of a subspace.

Part C: For each of the following subsets, do the following: 1. Let :'Lbe a subset of the vector space R4, where T is the set of all vectors of the form ah 2a+4b 1 3a+5b and \"Mb are real numbers. Identify which properties of a subspace are satised an not satised. Justify each claim with a proof or counterexample. 1. The zero vector is not in set T We 2 D and b = 0. (111 00 0 2a+4b _ 2(0)+4(U) _ e 1 _ 1 _ 1 3a+5b 3(U)+5(o) e 2. Set T is closed under vector addition. If vector (1 and vector m are in vector space R4, then dim, are in vector space R4. ab xy 2x 4 Vector d = 2n + 4b Vector m = 1- y 1 3a+5b 3X+5LV where a, b, x, and y are all real numbers a-b x -y ] a-b+x-y 2a + 4b 2x + 4y 1 + 2a + 4b + 2x + 4y 1 1+1 3a + 5b] 3x + 5y] [3a + 5b + 3x + 5y] a- b+x-y 2a + 4b + 2x +4y 2 E R4 because they are all some real number [3a + 5b + 3x + 5y) 3. Set T is not closed under scalar multiplication. Scalar is c, where a, b, and c is any real number PERTIES AND CHARACTERISTICS 9 a-b ac - bc C 2a + 4b 2ac + 4bc 1 = C [3a + 5b. 3ac + 5bc] T is not closed under scalar multiplication because when c equals anything but 1 it is not in R4