Inner product generated by matrix

[derryck1234]

Homework Statement

Find d(u, v), where the inner product is defined by the matrix

[1 2]
[-1 3]

and u = (-1, 2), v = (2, 5)

Homework Equations

<u, v> = Au . Av
d(u, v) = abs(u - v)

The Attempt at a Solution

I first tried to find the resulting inner product from the matrix in terms of an equation:

I got it to be:

2u₁v₁ + 13u₂v₂

Then I simply found u - v, which came to be (-3, -3)

And thus d(u, v) = <-3, -3>^0.5

This, in terms of the relevant inner product, is:

[2(9) + 13(9)]^0.5

Unfortunately, the books answer does not agree? It says it is 3 times root 13. I get root 135?

 

[Office_Shredder]

Check your inner product calculation. There should be some u₁v₂ and u₂v₁ terms

 

[derryck1234]

Thanks.