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Choose one of the following problems and determine whether the given set (together with the usual...

Choose one of the following problems and determine whether the given set (together with the usual operations on that set) forms a vector space over R. In all cases, justify your answer carefully.

a. The set of all n x n matrices A such that A² is symmetric.

b. The set of all points in R² that are equidistant from (-1, 2) and (1, -2)

c.  The set of all polynomials of degree 5 or less whose coefficients of x² and x³ are zero.

you can choose any

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