Let {f1, f2, ., fn} be an orthonormal basis of an inner product space V , and let v = > a¿f¡ and .... w = > b;fi , where ai, bị E R. i=1 (a) Show that (v, w ) Ea;b;. i=1 (b) Show that || v||2 =E a?. i=1 =WI

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
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[Linear Algebra] How do you prove this?

Let {f1, f2,
..., fn} be an orthonormal basis of an inner product space V , and let v =
Eazf; and
i=1
n
> b;fi , where ai, bị E R.
w =
i=1
n
(a)
Show that (v, w)= > a;b¿.
W
i=1
n
(b)
Show that ||v||2
Σ.
i=1
Transcribed Image Text:Let {f1, f2, ..., fn} be an orthonormal basis of an inner product space V , and let v = Eazf; and i=1 n > b;fi , where ai, bị E R. w = i=1 n (a) Show that (v, w)= > a;b¿. W i=1 n (b) Show that ||v||2 Σ. i=1
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