8. Suppose that V is a subspace of the 1vector spaoe W. Assume that dimlW} n: dith} I. Show there exists a \"actor subspace U of W, containing 1."? such that V at U 5:9 W. 9. Show that if V is a subspace of a mute-dimensional vector space W and dtm(V) = dimtf}? than V = HI. ID. Prove that whenever H is a subspace of a nite-dimensional vector space V, diml} if. di-me}. 11. Asmmc that U and W are subspaces of a vector space V. If dim{U] + dimiIW] 3= atmv'}, prove that U H W 9-9 {}