I've been given this problem and I really don't know how to approach it.
Suppose an inner product defined on R^2 has the values <(-1,2),(-1,2)> = 2, <(2,5),(2,5)> =3 and <(-1,2),(2,-5)>=5. Calculate the lengths ||e1|| and ||e2|| of the standard basis vectors for the length function associated with the given inner products. Hint: express e1 and e2 in terms of the vectors (-1,2) and (2,-5) and use homogeneity and additivity of the inner product.
Any help would be appreciated.