Let x and y be vectors in R4; let v and w be vectors in R3, and let A be a 4 times 3 matrix. Determine whether each of the following quantities are a scalar, a vector (in which case you should say if it belongs to R3 or R4), a matrix (in which case you should give its size), or nonsense. For the purposes of this problem, matrices with a single column should be called vectors. x middot x x middot x middot x (x middot x) middot x (x middot x)x (x + 2y) middot y v middot Ax Av middot Aw x middot ATy (v middot w) Ax A((x middot y) Aw middot y) dist(x, x) ||2y + x|| ||y||y ||w||x dist(w, 2v) A dist(x, w)y middot x