Question

Determine whether the given set S is a subspace of the vector space V. A. V = R^2, and S consists of all vectors (x1, x2) satisfying x1^2 - x2^2 = 0. B. V = Mnxn(R), and S is the subset of all upper triangular matrices. C. V = R^n, and S is the set of solutions to the homogeneous linear system Ax = 0 where A is a fixed m x n matrix. D. V = Mnxn(R), and S is the subset of all n x n matrices with det(A) = 0. E. V is the vector space of all real-valued functions defined on the interval (-?, ?), and S is the subset of V consisting of those functions satisfying f(0) = 0. F. V = Pn, and S is the subset of Pn consisting of those polynomials satisfying p(0) = 0. G. V = C^1(R) (continuously differentiable functions), and S is the subset of V consisting of those functions satisfying f'(0) ? 0.

          Determine whether the given set S is a subspace of the vector space V.

A. V = R^2, and S consists of all vectors (x1, x2) satisfying x1^2 - x2^2 = 0.
B. V = Mnxn(R), and S is the subset of all upper triangular matrices.
C. V = R^n, and S is the set of solutions to the homogeneous linear system Ax = 0 where A is a fixed m x n matrix.
D. V = Mnxn(R), and S is the subset of all n x n matrices with det(A) = 0.
E. V is the vector space of all real-valued functions defined on the interval (-?, ?), and S is the subset of V consisting of those functions satisfying f(0) = 0.
F. V = Pn, and S is the subset of Pn consisting of those polynomials satisfying p(0) = 0.
G. V = C^1(R) (continuously differentiable functions), and S is the subset of V consisting of those functions satisfying f'(0) ? 0.

Determine whether the given set S is a subspace of the vector space V.

A. V = R^2, and S consists of all vectors (x1, x2) satisfying x1^2 - x2^2 = 0.
B. V = Mnxn(R), and S is the subset of all upper triangular matrices.
C. V = R^n, and S is the set of solutions to the homogeneous linear system Ax = 0 where A is a fixed m x n matrix.
D. V = Mnxn(R), and S is the subset of all n x n matrices with det(A) = 0.
E. V is the vector space of all real-valued functions defined on the interval (-?, ?), and S is the subset of V consisting of those functions satisfying f(0) = 0.
F. V = Pn, and S is the subset of Pn consisting of those polynomials satisfying p(0) = 0.
G. V = C^1(R) (continuously differentiable functions), and S is the subset of V consisting of those functions satisfying f'(0) ? 0.

Added by Larry V.

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