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
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4f6a9e3-aa41-47b6-b1d1-b71278e16cd7%2F809c1af5-a0fa-4787-b987-00d4b07df758%2Fa9ekd5q_processed.jpeg&w=3840&q=75)
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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