Let I2 and = in R', we have 43, () (u, v) uv:= x1y1 + 122 + 3Y3. Let ui = and Uz = Show that B = (u1, U2, u3) is linearly independent set in R. Show that B = (1, u2, u3) is a spanning set of R. Deduce that B is a basis of R. %3D orthonormal basis

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let E R be a Euclidean space equiped with the dot product, i.e., for all
%3D
I2
and =
Y2
in R, we have
I3
43,
and
(u, v) = u v:= 11y1 + 122 + 3Y3. Let ui =
uz =
Show that B = (u, u2, u3) is linearly independent set in R.
Show that B = (1, u2, u3) is a spanning set of R.
Deduce that B is a basis of R.
%3D
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, i.e., for all %3D I2 and = Y2 in R, we have I3 43, and (u, v) = u v:= 11y1 + 122 + 3Y3. Let ui = uz = Show that B = (u, u2, u3) is linearly independent set in R. Show that B = (1, u2, u3) is a spanning set of R. Deduce that B is a basis of R. %3D By using the Gramm-Schmidt procedure determine an orthonormal basis from B.
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