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Show that B= (u1, u2, u3) is linearly independent set in R. Show that B = (u1, u2, U3) is a spanning set of R°. Deduce that B is a basis of R³. %3D

Show that B= (u1, u2, u3) is linearly independent set in R. Show that B = (u1, u2, U3) is a spanning set of R°. Deduce that B is a basis of R³. %3D

Advanced Engineering Mathematics
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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Exercise and v = Y2 Let E = R³ be a Euclidean space equiped with the dot product, i.e., for all u = Y3, in R3, we have ()--()-- (3) and uz = , U2 = (u, v) = u - v := 11Y1+T2Y2 + T3Y3. Let u1 = 1- Show that B= (u1, u2, uz) is linearly independent set in R. 2- Show that B = (u1, u2, Uz) is a spanning set of R'. 3- Deduce that B is a basis of R°. 4- By using the Gramm-Schmidt procedure determine an orthonormal basis B, from B.
Transcribed Image Text:Exercise and v = Y2 Let E = R³ be a Euclidean space equiped with the dot product, i.e., for all u = Y3, in R3, we have ()--()-- (3) and uz = , U2 = (u, v) = u - v := 11Y1+T2Y2 + T3Y3. Let u1 = 1- Show that B= (u1, u2, uz) is linearly independent set in R. 2- Show that B = (u1, u2, Uz) is a spanning set of R'. 3- Deduce that B is a basis of R°. 4- By using the Gramm-Schmidt procedure determine an orthonormal basis B, from B.
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