Which of the following are actually vector spaces over the r

Which of the following are actually vector spaces over the real numbers? The complex numbers The set of all polynomials of even degree. All continuous functions for which integral^1_0 f(x) dx =0. All vectors of the form (a, b, l) where a and b are any real numbers. I & II I&III; I & IV II & III II & IV The mathematica command \"RowReduce[] is a very useful tool in solving a system of linear equations. finding the inverse of a matrix. finding the dimension of the range of a transformation. computing the determinant of a matrix. determining if a set of vectors is linearly independent. I only I & II only I, II & III only All but IV All but V

Solution

3. The statements I and III are correct because complex numbers form a vector space as well as all coontinuous functions form a vector space

4. Row reduce is very usful tool in solving system of liner equations and finding the inverse of a matrix. So statement I and II are correct.