## Elementary Linear Algebra 7th Edition

Assume that the matrix $A$ is given by $$A=\left[\begin{array}{cc}{x_1} &{x_2} \\{x_3}& {x_4} \end{array}\right],$$ then we have the system \begin{aligned} x_{1}+x_{3}&=1 \\ x_{2} +x_4 &=0\\ x_1+x_{3} &=0\\ x_{2} +x_4 &=1 \end{aligned}. It easy to see that the above system is not consistent since it gives $0=1$ which is a contradiction.