Science:Math Exam Resources/Courses/MATH221/December 2019/Question 01 (a)/Statement

Consider the linear system

$${\begin{aligned}-6x_{1}+6x_{2}-11x_{3}-3x_{4}=&-12\\2x_{1}-2x_{2}+2x_{3}-4x_{4}=&14\\x_{1}-x_{2}-5x_{4}=&13\\3x_{1}-3x_{2}+6x_{3}+3x_{4}=&3\end{aligned}}$$

State whether this system is consistent or inconsistent. If it is consistent, write down the set of solutions in parametric vector form. If it is inconsistent, explain how you can tell.