SOLUTION: Using the properties of the Euclidean inner product, prove the parallelogram identity, a+b∥^2 +∥a−b∥^2 =2∥a∥^2 +2∥b∥^2

Algebra ->  College  -> Linear Algebra -> SOLUTION: Using the properties of the Euclidean inner product, prove the parallelogram identity, a+b∥^2 +∥a−b∥^2 =2∥a∥^2 +2∥b∥^2      Log On


   

Question 1165795: Using the properties of the Euclidean inner product, prove the parallelogram identity, a+b∥^2 +∥a−b∥^2 =2∥a∥^2 +2∥b∥^2
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
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Using properties and definition of the scalar product of vectors, you have


  ||a+b||^2 = ||a||^2 + 2*(a,b) + ||b||^2

  ||a-b||^2 = ||a||^2 - 2*(a,b) + ||b||^2


Now add these two identities, and you will get the statement which has to be proved.

Solved.