(41) If A BC, then R(A) C R(B). (42) Let A be an m x n matrix and Ban n x p matr
ID: 3033654 • Letter: #
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(41) If A BC, then R(A) C R(B). (42) Let A be an m x n matrix and Ban n x p matrix. If C AB, then EIR") (43) The linear span of the vectors (4,0, 0,1), (0, 2,0, -1) and (4,3, 2, 1) is the 3-plane a 1 -2z2 3:3 4.a4 0 in R (44) The linear span of the vectors (4, 0, 0, 1), (0,3, 2,0) and (4, 3, 2, 1) is the 3-plane z 2a2 3z3 -414 0 in R (45) Let u, v, and w be vectors in Ri Then spantu, v, wh span{ u 2v, u (46) The set Iz1, a2, ara, z4) Iz1 a3 T2 -zM -0) is a subspace of R (47) The set fri, ac2, z3, z4) I z1 +z3 -z2 zA 1) is a subspace of R (48) Every subspace of R" has an orthogonal basis. (49) Every subspace of R" has an orthonormal basis.Explanation / Answer
41. The statement is False.
44. The statement is False.
45. The statement is True.
46. The statement is True.
47. The statement is False.
48. The statement is True.
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