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12 Nov 2019
a) Determine if S = {(x, y) elementof R^2, 3xy - 5y = 0} is a subspace of R^2. Justify your answer. b) Determine if S = {(x, y) elementof R^2, 2x - 7y = 0} is a subspace of R^3. Justify your answer.
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Keith Leannon
Lv2
1 Nov 2019
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Let A be an m times n matrix. Prove that the nullspace of A, N(A) = {x elementof R^n: Ax = 0, is a subspace of R^n.: Ax = 0}, is a subspace of R^n.
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Let A be an m times n matrix. Prove that the nullspace of A, N(A) = {x elementof R^n: Ax = 0, is a subspace of R^n.: Ax = 0}, is a subspace of R^n.
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For each of the sets S below, determine whether or not it is a subspace of Rn. If itis not, show that it fails one of the three defining axioms of a subspace. If it is express it as the span of a set of vectors. (a) S={(x, y, z > w): w greaterthanorequalto 0}. (b) S={(x, y, x* + y2): x, y elementof R}. (c) S is the union of the lines L_1 = {x + y = 0} with L_2 = {x - y = 0}. (Thus a point (x, y) elementof R2 lies in S if and only if it lies in either L_1 or L_21.) (d) S is the intersection of the planes P_1 = {x y z = 0} and P2 = {x y - z = 0}. (Thus a point lies in S if and only if it lies in both P_1 and P_2)
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