determine whether the given set ss is a subspace of the vector space vv a vp2vp2 and ss is the s

1. Closure under addition: Let $p_1(x) = x^2 + c_1$ and $p_2(x) = x^2 + c_2$ be two polynomials

Question

Determine whether the given set S is a subspace of the vector space V. A. V = P2, and S is the subset of P2 consisting of all polynomials of the form p(x) = x^2 + c. B. V = C5(I), and S is the subset of V consisting of those functions satisfying the differential equation y^(5) = 0. C. V is the vector space of all real-valued functions defined on the interval [a, b], and S is the subset of V consisting of those functions satisfying f(a) = f(b). D. V = C3(I), and S is the subset of V consisting of those functions satisfying the differential equation y''' + 7y = x^2. E. V = Mn(R), and S is the subset of all symmetric matrices. F. V = Rn, and S is the set of solutions to the homogeneous linear system Ax = 0, where A is a fixed m x n matrix. G. V = R2, and S consists of all vectors (x1, x2) satisfying x1^2 - x2^2 = 0.

          Determine whether the given set S is a subspace of the vector space V.
    
    A. V = P2, and S is the subset of P2 consisting of all polynomials of the form p(x) = x^2 + c.
    
    B. V = C5(I), and S is the subset of V consisting of those functions satisfying the differential equation y^(5) = 0.
    
    C. V is the vector space of all real-valued functions defined on the interval [a, b], and S is the subset of V consisting of those functions satisfying f(a) = f(b).
    
    D. V = C3(I), and S is the subset of V consisting of those functions satisfying the differential equation y''' + 7y = x^2.
    
    E. V = Mn(R), and S is the subset of all symmetric matrices.
    
    F. V = Rn, and S is the set of solutions to the homogeneous linear system Ax = 0, where A is a fixed m x n matrix.
    
    G. V = R2, and S consists of all vectors (x1, x2) satisfying x1^2 - x2^2 = 0.

Added by Robert M.

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