Question. 3 {x₁,x₂,.,x} is a subset of an Inner Product space. Suppose that X = a. If X is an orthogonal set, show that |x₁ + x₂ + ... + x₂|² = |x₁|² +|x₂|² + ···+|x₂|² b. If X is an orthonormal set, then x₁ + x₂ ++x² = =?
Question. 3 {x₁,x₂,.,x} is a subset of an Inner Product space. Suppose that X = a. If X is an orthogonal set, show that |x₁ + x₂ + ... + x₂|² = |x₁|² +|x₂|² + ···+|x₂|² b. If X is an orthonormal set, then x₁ + x₂ ++x² = =?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 29E
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Transcribed Image Text:Question. 3
{x₁,x₂,...,x} is a subset of an Inner Product space.
Suppose that X =
a. If X is an orthogonal set, show that |x₁ + x₂ + ... + x₂|² = |x₁|² +|x₂|² + ... + x ₂ ²
b. If X is an orthonormal set, then |x₁ + x₂ + ··· + x₂ ³²³
= ?
2
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