Please solve this.

(4) (10 marks) The Grassmannian G = Gr(2,3) is the set of planes through the origin (i.e. 2-dimensional vector subspaces) in 3-dimensional space. The goal of this problem is to show this is an (abstract) smooth surface in two different ways. (a) (4 marks) Show that each plane can be specified by a point in the real projective plane RP2. (b) (6 marks) We can represent a plane V E G by a full rank 2 x3 matrix My, where the row vectors of My are a basis for V. Subsequently, for any invertible 2 x 2 matrix A, the product AMy defines the same point in G as it corresponds to changing the basis for V. Show that G can be covered by the image of the three maps: O 0 0 UI(u, v) = V U2 (u, v ) = U3 ( u, V) = u 0 v where u, v E R. Hint: The image of Us is in row-reduced echelon form