(38) {3u-2v, 2v -4u, Aug -3u is linearly dependent for all choices of u, v, and
ID: 3033650 • Letter: #
Question
(38) {3u-2v, 2v -4u, Aug -3u is linearly dependent for all choices of u, v, and (39) Every set of orthogonal vectors in Rn is linearly independent. (40) If A BC, then every solution to Ca 0 is a solution to Ar 0. (41) If A BC, then R(A) CR(B). (42) Let A be an m x n matrix and B an n x p matrix. If C AB, then (43) The linear span of the vectors (4,0,0, 1), (0,2, 0, -1) and (4,3,2, 1) is the 3-plane aar1 2a2 +3a3 -4zA 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 0 in IR (45) Let u, y, and be vectors in R Then span Lu, 1, span u+ 2v, (46) The set tri, a2, a3, 4) l zi +z3 r2 -z4 0) is a subspace of R (47) The set tri, a2, z3, ars) z1 +z3 z2 a4 1) is a subspace of R (48) Every subspace of R" has an orthogonal basis. (49) Every subspace of R" has an orthonormal basis. 11 Span (50) spanExplanation / Answer
(38) Since 4w -3u = -(3u-2v)-(2v-4w), hence the given vectors are linearly dependent. The statement is True.
(39) The statement is True.
(40) The statement is True (Ax = BCx = B(Cx) = B.0 = 0 if Cx = 0).
(41) The statement is False.
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