8. If A is an m x n matrix and b #0 is a vector in R", show that {z: Az = b} is not a subspace of R. 9(a) Show that the set P3 of polynomials of degree less than or equal to 3 is a subspace of the vector space of all polynomials. (b) Show that the set {p P3: p(1) = 0} of polynomials of degree 3 or less that have a root at z = 1 is a subspace of P3. (c) Show that the set {p P3 : p(1) = 4} of polynomials of degree 3 or less that have the value 4 at z = 1 is not a subspace of P3. 10(a) Is the set of polynomials whose graphs are symmetric around the y-axis, that is, (PEP: p(x) = p(-x) for all x}, a subspace of the vector space of all polynomials? (b) Is the set of polynomials of degree greater than or equal to 2 a subspace of the vector space of all polynomials? (c) Is the set of polynomials p such that f p(x) dx = 0 a subspace of the vector space of all polynomials?