I am supposed to determine whether or not the following two sets constitute a vector space. 1) The set of all polynomials degree two. 2) The set of all diagonal 2 x 2 matrices. For the first one, it will not be a vector space because it does not satisfy the closure property. Also the distributive property would be broken because a(x+y)^2 would not be (ax+ay)^2, or did I do that wrong? The second one would not satisfy additivity properties, and not be a vector space. Right? I don't know the set notation in LaTeX, so I'm not really sure how to put up much of my work.