(Solution) - a Prove that x 2 x v1 -(2025 Original AI-Free Solution)

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(a) Prove that
(( x ((2 ( ( x ( v1 (2 + ( x ( v2 (2 + ( ( ( + ( x ( vk (2
(This inequality is called Bassel's Inequality.)
(b) Prove that Bessel's Inequality is an equality if and only if x is in span (S).

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