linear algebra proofthanks Problem 7: Let €₁, €2,.en,... be an infinite list of orthonormal vectors in V. Letv € V and let a₂ = (v, ei). Show that the seriesconverges.Let UN=2Σlai1²i=1Span(e₁,e2,..., ey). Suppose thatlim ||v Pru (v)|| = 0.N→∞Show that the series in (2) has sum equal to ||v||².(2)

There are two parts to the question. In the first part, it is required to show that ∑i=1∞ai2…

Answered: Problem 7: Let €1, €2, . . . , ¤n,…. be…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.3: The Addition And Subtraction Formulas

Problem 80E

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linear algebra proof

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Problem 7: Let €₁, €2,.
en,... be an infinite list of orthonormal vectors in V. Let
v € V and let a₂ = (v, ei). Show that the series
converges.
Let UN
=
2
Σlai1²
i=1
Span(e₁,e2,..., ey). Suppose that
lim ||v Pru (v)|| = 0.
N→∞
Show that the series in (2) has sum equal to ||v||².
(2)

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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