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Let E R be a Euclidean space equiped with the dot product, i.e., for all %3D u = I2 and = in R, we have 43 u, v) = uv:= 141 + r22 + 3y3 Let u = 2 and 1 Uz = 1- Show that B = (u1, u2, u3) is linearly independent set in R. 2- Show that B = (u1, u2, u3) is a spanning set of R. 3- Deduce that B is a basis of R %3D %3D

Let E R be a Euclidean space equiped with the dot product, i.e., for all %3D u = I2 and = in R, we have 43 u, v) = uv:= 141 + r22 + 3y3 Let u = 2 and 1 Uz = 1- Show that B = (u1, u2, u3) is linearly independent set in R. 2- Show that B = (u1, u2, u3) is a spanning set of R. 3- Deduce that B is a basis of R %3D %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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Let E = R be a Euclidean space equiped with the dot product, i.e., for all I2 and = in R, we have 43 u, v) = uU:= Ty1 + 122 + 33- Let ui = and Uz = 1- Show that B = (u1, u2, u3) is linearly independent set in R. 2- Show that B = (u1, u2, u3) is a spanning set of R. 3- Deduce that B is a basis of R. %3D 4- By using the Gramm-Schmnidt procedure determine an orthonormal basis B, from B.
Transcribed Image Text:Let E = R be a Euclidean space equiped with the dot product, i.e., for all I2 and = in R, we have 43 u, v) = uU:= Ty1 + 122 + 33- Let ui = and Uz = 1- Show that B = (u1, u2, u3) is linearly independent set in R. 2- Show that B = (u1, u2, u3) is a spanning set of R. 3- Deduce that B is a basis of R. %3D 4- By using the Gramm-Schmnidt procedure determine an orthonormal basis B, from B.
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