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po Determine whetherthe ghven set s a ubapace df he vtor spcv A. V = P21, and s

ID: 3168913 • Letter: P

Question

po Determine whetherthe ghven set s a ubapace df he vtor spcv A. V = P21, and s is the subset of P2 consisting of all polynomials of the form p(x) = x2 + c. B. 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/(a) =f(b). C. V = Mn(R), and S is the subset of all n × n matrices with det(A) = 0. D.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. E. V- C(D, and S is the subset of V consisting of those functions satisfying the differential equation E V = C5(1), and S is the subset of V consisting of those functions satisfying the differential equation y(5)-0 G.V Mn(R), and S is the subset of all skew-symmetric matrices.

Explanation / Answer

1

0

1

0

and B =

0

1

0

-1

so that A+B=

1

1

1

-1

Then det(A) =0, det(B)=0 ,but det(A+B) = -20. Thus, A and B S , but A+B S. Hence S is not closed under vector addition, and therefore, S is not a subspace of V = M2(R).

Please post the parts E,F,G again, separately.

1

0

1

0