2. Let A = bmatrix 1 & -1 & 2 & 1 & 1 \ 1 & -1 & 2 & 2 & 1 \ 1 & -1 & 4 & 1 & 1 \ 1 & -2 & 2 & 1 & 1 \ -2 & 2 & -4 & -2 & 1 bmatrix. Find the inverse of $A$. (10%)

2. Let the $ f(\theta) = \frac{n!}{(n - x)!x!}\theta^x (1 - \theta)^{n - x}, x < n $, be the function of $ \theta \in [0,1] $. Denoted $F(\theta) = \log f(\theta)$, where x and n are the positive, fixed constants. Show that $x/n$ is the unique critical point that is a maximizer of $F$ concerning $\theta$. (15%)