Compute the first two iterates $\mathbf{x}^{(1)}$, $\mathbf{x}^{(2)}$ using Broyden's Method for the initial point $\mathbf{x}^{(0)}=(1,4)$ and the function $f(x_{1},x_{2})=3x_{1}^2+x_{2}^2-x_1x_2$ with $D_0=I$.
Does this question even make sense? To my understanding in this case we need two equations as input. I.e. $f(x)$ be a system of equations $f_1(x_1,x_2)$ and $f_2(x_1,x_2)$. Otherwise applying the method we end up getting a vector equal to a scalar.