Show that the vectors u₁ = (3, 1,-4),= (3,1, –4), u₂ = (2,5,6), andu} == (1, 4, 8) form a basis in R³. Find the coordinates of (1, 1, 1)in this basis.

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Answered: Show that the vectors u₁ = (3, 1,-4), =…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let u = (1,3, 5) and v = (-4,3, –7) be vectors in R3. (a) Find u + v. (b) Express u in terms of the standard basis vectors in R3. (c) Find -3u.
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Show that the vectors u₁ = (3, 1,-4), = (3,1, –4), u₂ = (2, 5, 6), and u} = = (1, 4, 8) form a basis in R³. Find the coordinates of (1, 1, 1) in this basis.