14a.Show that the vectors w₁ = (0,2,0), W₂ = (3,0,3), W3 = (-4,0,4) form an orthogonal basis for R³ with the Euclidean inner product and use that basis to find an orthogonal basis by normalizing each vector. b. Express vector u = (1,2,4) as a linear combination of the orthonormal basis vectors obtained in part (a)

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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14a. Show that the vectors w₁ = (0,2,0), W₂ = (3,0,3), W3=(-4,0,4) form an orthogonal
basis for R³ with the Euclidean inner product and use that basis to find an orthogonal basis by
normalizing each vector.
b. Express vector u = (1,2,4) as a linear combination of the orthonormal basis vectors obtained in
part (a)
Transcribed Image Text:14a. Show that the vectors w₁ = (0,2,0), W₂ = (3,0,3), W3=(-4,0,4) form an orthogonal basis for R³ with the Euclidean inner product and use that basis to find an orthogonal basis by normalizing each vector. b. Express vector u = (1,2,4) as a linear combination of the orthonormal basis vectors obtained in part (a)
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