Prove there exists a positive number c such that two inner products with corresponding norms?

See explanation below

Step-by-step explanation:

We assume that we have two inner products on v such that if and only if and we want to proof is there is a positive number c like this :

for every in V

We can assumee that we have an orthonormal basis of V with respect . We can define the following sets:

both defined on a n dimensional space, and then we have that for any linear comibnation we have this:

And A neds to be a matrix with entries

So then we have this:

And then we have the maximum defined and we need to satisfy that c is the maximum value for te condition required.

for every in V

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)

x = 12

y = 1

for the points!