2. (10) Suppose we are trying to unde rstand the behavior of a mysterious alien computer we found while exploring the Martian wasteland. Strangely enough, it has a number pad hen we enter a number, the computer responds with another number. Our commander has asked us to try to model the relationship between inputs and outputs, and our-best guess is that the function matches a polynomial of the form with digits -1,0, and 1. W uu2x + u3a2. We have the following sequence of inputs and outpu x 1 01 0 p(x)0 1 -1 0 (a) Formulate the problem of finding u2and(3o best match the data as a least- squares problem. What are A and b? (b) Find the p(x) that most closely matches our observed data in the least-squares sense and calculate the^2-norm error between the observed output and the output calculated by p(). The following matrix may be useful to you 0.5 0-0.5 0 2 0 -0 0.5 0 -0.5 0 1