2. Explain why the following sets are not vector spaces. 3 / 4 al The set of polynomials of degree ?. { ( IP= azz+ but c, abic E /R] Let U= KX, V= Kx (KE IR ) utv= ke' t / (-kx?)=0 O is not degree 2 polynomial under vector addition not a vector space where did this come (b) The set of all rational numbers. from ? Let C = 1 2 u = 1 ca = NZ. 1 = VZ I rational number not close under scalar multiplication not a vector space. Let V be the set of all circles in Ra centered at the origin. Interpret the origin to be an element of V (a circle of radius zero). Let C, and 2 be elements of V. Define C1 + C2 to be the circle centered at the origin whose radius is the sum of the radii of C, and C2. Define KC_1 to be the circle centered at the origin whose radius is | k | times that of C1. If This moans handle = 0. Explain why V is not a vector space. V = = C / c = ( x-h ) + ( y - K)= x2, h,k, relks ( x-h )? + ( y-K ) Z ( ex-h)+ ( y-k)] not under vector addition. not a vector space