Please help correct my work

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- September 21st 2012, 08:26 AMangelmePlease help check my solutions for vector space questions
**Please help correct my work**

Attachment 24869

Attachment 24870 - September 21st 2012, 10:46 AMPlatoRe: Please help check my solutions for vector space questions
From looking at the images you posted it seems that you are proving:

The standard proof follows from the fact where is the angle between the two non-zero vectors .

Then note that - September 21st 2012, 01:34 PMDevenoRe: Please help check my solutions for vector space questions
first of all, you have and wrong.

while:

, as well.

thus:

.

on the other side of the inequality we have:

since , we indeed have for these particular U,V:

.

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for your second problem, you are also calculating the norms of U and V incorrectly. use the definition of the inner product you are given! - September 21st 2012, 06:05 PMangelmeRe: Please help check my solutions for vector space questions
Thank you so much!! Deveno! I missed the obvious point

Could you please re-check my second answer again?

Attachment 24877 - September 22nd 2012, 12:30 PMDevenoRe: Please help check my solutions for vector space questions
still incorrect. for starters, you have an extra 2

^{-n}term in and .

secondly, you don't seem to get that the inner product of two vectors should be a SCALAR, not an "expression".

so for U, you should have:

and for V, you should have:

while for the dot product, you should have: