3, 14 gives a basis for W (a) ₁ = (1,1,1,2,3), ₂ = (1,2,-1, -2, 1), uz (3,5,-1, -2,5), u = (1.2, 1,-1,4) = span(u) of R³, where

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Chapter2: Second-order Linear Odes
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4.97. Find a subset of u₁, 12, 13, 14 that gives a basis for W = span(u,) of R³, where
-
(a) u₁ = (1,1,1,2,3), u₂ = (1,2,-1, -2, 1), uz
(b) ₁ = (1, -2,1,3,-1), u₂ = (-2,4, -2, -6,2),
(c) u₁ = (1,0, 1, 0, 1), 1₂ = (1, 1, 2, 1,0),
(d) ₁ = (1,0, 1, 1, 1), u₂=(2, 1, 2, 0, 1),
(3,5,-1, -2,5), U4 = (1,2,1,-1,4)
z = (1, -3, 1, 2, 1), u4=(3,-7, 3, 8, -1)
4(1,2,1, 1, 1)
u =(4,2,5,4,6)
u3 = (2, 1, 3, 1, 1),
u3 = (1, 1,2,3,4),
Transcribed Image Text:4.97. Find a subset of u₁, 12, 13, 14 that gives a basis for W = span(u,) of R³, where - (a) u₁ = (1,1,1,2,3), u₂ = (1,2,-1, -2, 1), uz (b) ₁ = (1, -2,1,3,-1), u₂ = (-2,4, -2, -6,2), (c) u₁ = (1,0, 1, 0, 1), 1₂ = (1, 1, 2, 1,0), (d) ₁ = (1,0, 1, 1, 1), u₂=(2, 1, 2, 0, 1), (3,5,-1, -2,5), U4 = (1,2,1,-1,4) z = (1, -3, 1, 2, 1), u4=(3,-7, 3, 8, -1) 4(1,2,1, 1, 1) u =(4,2,5,4,6) u3 = (2, 1, 3, 1, 1), u3 = (1, 1,2,3,4),
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