## Question

###### Linear algebra: 12. (5 points) Show that ((ui, U2, U3), (01, 02, 03)) = U101 -...

linear algebra:

12. (5 points) Show that ((ui, U2, U3), (01, 02, 03)) = U101 - U2U2 - UzU3 is not an inner product on R3.

## Answers

It doesn't satisfy one condition of inner product which is given below in details. That's why it is not an inner product.

<(ly, ų, ug), (1,02, )) = we run 2 - ug 03 product that me know ichnere Fore the Let Then ca, a> o if azo. x=(1,1,1) (a,0) = {(1,1,1), (1,1,1) = 1-1-1 -- 1 co it violest the the condition (x,x)o if so ato So L(41, 42, 4), (1, Uqus)) = 44, - hq Cq - Ug Us product. is not an inner

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