Haven

2021-09-22

The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x, y;x,y; or x, y, z;x,y,z; or ${x}_{1},{x}_{2},{x}_{3},{x}_{4}$ as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution.
$\left[\begin{array}{cccccc}1& 0& 0& 0& |& 1\\ 0& 1& 0& 0& |& 2\\ 0& 0& 1& 2& |& 3\end{array}\right]$

dieseisB

The goal of the task is to write a system of equations that corresponds to a given matrix. And then determine whether the system is consistent or not and if so give a solution.
The system that corresponds to a given matrix is:
$\left\{\begin{array}{l}1\cdot {x}_{1}+0\cdot {x}_{2}+0\cdot {x}_{3}+0\cdot {x}_{4}=1\\ 0\cdot {x}_{1}+1\cdot {x}_{2}+0\cdot {x}_{3}+0\cdot {x}_{4}=2\\ 0\cdot {x}_{1}+0\cdot {x}_{2}+1\cdot {x}_{3}+2\cdot {x}_{4}=3\end{array}$
$\left\{\begin{array}{l}{x}_{1}=1\\ {x}_{2}=2\\ {x}_{3}+2{x}_{4}=3\end{array}$
The system is consistent.
${x}_{1}=1,{x}_{2}=2,{x}_{3}+2{x}_{4}=3,{x}_{3}=3-2{x}_{4}$
${x}_{4}$ is real number

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