WeBWork Linear Algebra - Section 3.2 Subspaces - Section 3.2 Subspaces Which of the following subsets of R^3x3 are subspaces of R^3x3 A The 3x3 matrices

WeBWork Linear Algebra - Section 3.2 Subspaces - Section...

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Section 3.2 Subspaces Which of the following subsets of R^3x3 are subspaces of R^3x3? A. The 3x3 matrices whose entries are all greater than or equal to 0 B. The 3x3 matrices whose entries are all integers. C. The symmetric 3x3 matrices. D. The diagonal 3x3 matrices E. The non invertible 3x3 matrices F. The 3x3 matrices with all zeros in the second row Solution = CDF Determine whether the given set S is a subspace of the vector space V. A. V=R^nxn and S is the subset of all symmetric matrices. B. V=C1(R), and S is the subset of V consisting of those functions satisfying fprimed(0)>=o. C. V=R^nxn and S is the subset of all nonsingular matrices. D. 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). E. V=R^n and S is the set of solutions to the homogenous linear system Ax=0 where A is a fixed m x n matrix. F. V=P2, and S is the subset of P2 consisting of all polynomials of the form p(x)=x^2+c G. V=P4 and S is the subset of P4 consisting of all polynomials of the form
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