For x = (x₁,...,xn), y = (y₁,..., yn) R", define (x, y) = -1 j²xjYj.(a) Show that (,) is an inner product on R".(b) Suppose that n = -2, and draw the unit ball B = {x € R² :||x|| ≤ 1} (where || || is the norm derived in the usual way fromthe inner product (,)).

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2: Let a function d: R2 x R? →R defined by d(x, y) = ((x1 – y1)² + (x2 - y2)?) Vx = (x1, x2), y = (y1, Y2) E R2, then d be a %3D metric function on R2.
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For x = (x₁,...,xn), y = (y₁,..., yn) R", define (x, y) = -1 j²xjYj. (a) Show that (,) is an inner product on R". (b) Suppose that n = -2, and draw the unit ball B = {x € R² : ||x|| ≤ 1} (where || || is the norm derived in the usual way from the inner product (,)).