11. A property that must be satised by the elements of V under the addition operation + in a vector space is that of closure: Ifu, v e V , then ll + v e V. Determine whether elements of the given set satisfy the closure property under the dened addition operation +. A) V = Set of all real-valued differentiable functions on (00, co). + is the usual addition of lnctions. B) V = Set of all 2 x 2 matrices that have determinant different from zero. + is the usual addition of matrices. C) V = Set of all 2 x 2 matrices that have determinant equal to zero. + is the usual addition of matrices. 12. Let U, V, W be linear spaces. Prove that U m V n W is also a linear space. 13. Solve the linear equation Ax = b for the indicated matrices A and b. Justify. 2 AA1 >[3 l .p. \\_./ 0" H r\"\\ N rI \\..__/ 1 B)A= 0 4 1 2 3 [ CA.)[ [ D)A= mNHmMHomo Amm-hmmmom U H 1 2 3