0 43. Define g : V - RS, where V = Pi by g(ar + b) = b - a atb (a) Find the nullspace of g. (b) Find the nullity of g. (c) Find the range space of g. (Write it as a span) (d) What is the rank of g?(e) Use a nullity argument to determine whether g injective. (f) Use a rank argument to determine whether g surjective. 0 (g) Find a matrix representation of g : V -> RS, where V = Pi by g(ar + b) = b - a atb (h) Find a basis for the Column Space of this matrix.44. Define f : P2 - R? by f(ar + br + c) = atb (a) Find the nullspace of f. (b) Find the nullity of f. (c) Find the range space of f. (Write it as a span) (d) What is the rank of f?{e} Use a nullity argument to determine whether I injective. {f} Use a rank argument to determine whether I surjectivc. (g) Find a matrix representation of f :\"D; r [R2 by Her2 +31: + a] : ( :t: J. {h} Find a basis for the Column Space of this mntn'x. 45. Define T : M2x2 - R* by T b 2b d = (a) Find the nullspace of T. (b) Find the nullity of T. (c) Find the range space of T. (Write it as a span) (d) What is the rank of T?(e) Use a nullity argument to determine whether T injective. (f) Use a rank argument to determine whether T surjective. (g) Find a matrix representation of f : M2x2 - R' by f ( 2 2 ) = 2b -d (h) Find a basis for the Column Space of this matrix.30 0 0 1 0 0 0 (b) B = 020 The row reduced echelon form of B is 1 0 1 1 0 1 The nullity of B = The rank of B= A basis for the column space of B is The number of columns without leading entries is The number of leading entries (pivots) in the echelon form is Is the linear transformation represented by B injective, surjective, bijective? 1 0 1 0 0 0 10 (c) C= 2 2 The row reduced echelon form of C is 1 -1 0 0 0 The millity of C= The rank of C= A basis for the column space of C is The number of columns without leading entries is The number of leading entries (pivots) in the echelon form is Is the linear transformation represented by C injective, surjective, bijective