I could use some help with these problems in the picture.

(h) Let matrix A be a 15 x 20 matrix with rank r = 11. . The null space N(A) is a subspace of _ and dim N(A) = . The column space C(A) is a subspace of and dim C(A) = . The left null space N(A ) is a subspace of and dim N(A?) = . The row space C(A" ) is a subspace of and dim C(A") = 6. (5 points) Let V be the following subspace of R2 V = span { - [:] }- Find values for a, b E R such that V has dimension (a) zero (b) one (c) two 7. (5 points) Consider the subset of the set of all polynomials of degree at most 3, w - {p(x) | 2p(1) - 3p'(2) and p(2) - 1} c Ts . Show that W is not a subspace of the vector space Pa- Proof: 8. (15 points) Consider the two 3-dimensional vectors and w = Consider the subset of the set of all 2 x 3 matrices, V = A | 3AT = 2Aw C Matzx3 . (a) Show that V is a subspace of the vector space Mat2x3- Proof: (b) Find a basis for V. Basis for V: (c) What is the dimension of V? dim(V)=