DO NOT WANT AI SOLUTIONS. Thank you 1. Consider the mapping (,): R2 x R² → R defined by(u,v) = u³ Du, Vu, v € R²,where=»-(62)such that d1, d2 >0. Prove that (,) is an inner product.

Here's a proof that the given mapping defines an inner product on ℝ²: 1. Symmetry:To prove that we…

Answered: 1. Consider the mapping (,): R2 x R² →…

Linear Algebra: A Modern Introduction

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Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

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1. Consider the mapping (,): R2 x R² → R defined by (u,v) = u³ Du, Vu, v € R², where = »-(62) such that d1, d2 >0. Prove that (,) is an inner product.