P2 has a mysterious inner product * for which {x+4, 3x-5} is an orthonormal basis. IS there enough information to tell what is the length of 1? If so, compute it. If not say why not.
To determine the length of vector 1 in this scenario, we need more information about the inner product * defined on P2. The given information, {x+4, 3x-5}, only provides us with an orthonormal basis.
To find the length of vector 1, we must compute its inner product with itself. However, without knowing the specific definition of the inner product *, we cannot calculate this value. The inner product could potentially have various forms, such as the dot product or a custom-defined inner product. Each of these would yield different results when computing the length of vector 1.
Therefore, without further information about the inner product *, it is not possible to determine the length of vector 1.