QuestionFind the general solution for the system with the matrix:
$$\left[\begin{array}{rrrr} 0 & 1 & -2 & 2 \\ 1 & -4 & 6 & -5 \end{array}\right]$$
Choose A, B, C, or D for your answer.

Studdy Solution
We can see that $x_{3}$ is a free variable, which means it can take any real value. Therefore, the solution to the system is$$\left\{\begin{array}{l} x_{1}=4x_{2} -x_{3} -5 \\ x_{2}=2x_{3} +2 \\ x_{3} \text { is free } \end{array}\right.$$This corresponds to choice B in the given options.