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Let E - R' be a Euclidean space equiped with the dot product, ie., for all and v= in R', we have (u, r) = u = II + + 3s Let u = and () Show that B= (u, Wz, ug) is linearly independent set in R'. Show that B- (u1, #2, U3) is a spanning set of R'. Deduce that B is a basis of R. By using the Gramm-Schmidt procedure determine an orthonormal basis from B.

Let E - R' be a Euclidean space equiped with the dot product, ie., for all and v= in R', we have (u, r) = u = II + + 3s Let u = and () Show that B= (u, Wz, ug) is linearly independent set in R'. Show that B- (u1, #2, U3) is a spanning set of R'. Deduce that B is a basis of R. By using the Gramm-Schmidt procedure determine an orthonormal basis from B.

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, ie., for all u = and = 2 in R', we have {u, v) = u v:= 11 + 1y2 + 33. Let u = 2 and Show that B = (41, u2, u3) is linearly independent set in R. Show that B= (u1, u2, ug) is a spanning set of R". - Deduce that B is a basis of R. By using the Gramm-Schmidt procedure determine an orthonormal basis from B.
Transcribed Image Text:Let E = R' be a Euclidean space equiped with the dot product, ie., for all u = and = 2 in R', we have {u, v) = u v:= 11 + 1y2 + 33. Let u = 2 and Show that B = (41, u2, u3) is linearly independent set in R. Show that B= (u1, u2, ug) is a spanning set of R". - Deduce that B is a basis of R. By using the Gramm-Schmidt procedure determine an orthonormal basis from B.
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