Question: How do I go about part e) , f), and g)? 1. Which of the following are vector spaces over R (with respect to the

How do I go about part "e) , f), and g)"?

1. Which of the following are vector spaces over R (with respect to the standard addition and scalar multiplication)? If it is vector space, find its dimension. Justify your answers. a) S = {($1, 12, 13, 14) (R' | |+2 + 3 =0). b) S = {(21, 12, 13, ) ( R' | mi + 12 + 23 = 1}. c) S = {(21, 12, 13) ( R3 | 12 = 2x1 and x3 = 4x1}. d) The set of real-valued n x n matrices with nonnegative entries, where n is a given positive integer. e) The set of rational functions of the form 20. 1 : where p and q are polynomials in the complex variable s and the degree of q does not exceed a given fixed positive integer k. f) The space L'(R, R) of square-integrable functions, i.e., functions f : R - R with the property that 1so f2 (t)dt

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