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asn1 - MAT237Y Multivariable Calculus Summer 2009...

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MAT237Y – Multivariable Calculus Summer 2009 Assignment # 1 with corrections. Questions are worth 10 marks each. Due Tuesday, May 19, at 6:10pm sharp. 1. (a) Using the dot product, show that for x,y R n , the formula 2 bardbl x bardbl 2 + 2 bardbl y bardbl 2 = bardbl x + y bardbl 2 + bardbl x y bardbl 2 holds. (b) The norm on R n can be defined in terms of the dot product by the formula bardbl x bardbl = x x . Show that the reverse is true. That is, find a formula for x y involving the norms of vectors ( bardbl x bardbl , bardbl y bardbl , bardbl x + y bardbl , and bardbl x y bardbl for example), and without using coordinates.
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