The set of equations, $x_1 + 3x_2 = 17$, $5x_1 + 7x_2 = 19, and $11x_1 + 13x_2 = 23 has no real solution, but the pseudoinverse may be used to find close values. First, the matrix $A$ is set up: $A = \begin{bmatrix} 1 & 3\\ 5 & 7\\ 11 & 13 \end{bmatrix}$. We solve $A^\dagger = (A^TA)^{-1}A^T$ and get $A^\dagger = \begin{bmatrix} -0.5197 & -0.2171 & 0.2368\\ 0.4276 & 0.2039 & -0.1316 \end{bmatrix}$. Next, we find $\vec{x} = A^\dagger\vec{y}$ and multiply: $\begin{bmatrix} -0.5197 & -0.2171 & 0.2368\\ 0.4276 & 0.2039 & -0.1316 \end{bmatrix}$ $\begin{bmatrix} 17\\ 19\\ 23 \end{bmatrix} =$ $\begin{bmatrix} -7.51\\ 8.12 \end{bmatrix}$ This means $x_1 \approx -7.51$ and $x_2 \approx 8.12$.