Which of the following are actually vector spaces over the real numbers? The com

Question

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

Explanation / Answer

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.

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