Solve the least squares problem

$$\left[\begin{array}{ll} 1 & 3 \\ 0 & 2 \\ 0 & 2 \\ 0 & 1 \end{array}\right]\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]=\left[\begin{array}{r} 4 \\ 1 \\ 4 \\ -1 \end{array}\right]$$

using $Q R$ method with Householder transformation. (A solution using normal equations is not acceptable.)