Mathematics/Linear Algebra

row echelon form (ref), reduced row echelon form (rref)

Daniel-Kim 2011. 12. 21. 13:46

\begin{alignat}{7} 2x &&\; + \;&& y             &&\; - \;&& z  &&\; = \;&& 8 & \qquad (L_1) \\ -3x &&\; - \;&& y             &&\; + \;&& 2z &&\; = \;&& -11 & \qquad (L_2) \\ -2x &&\; + \;&& y &&\; +\;&& 2z  &&\; = \;&& -3 &  \qquad (L_3) \end{alignat}


row echelon form (ref)

\left[ \begin{array}{ccc|c} 2 & 1 & -1 & 8 \\ 0 & \frac{1}{2} & \frac{1}{2} & 1 \\ 0 & 0 & -1 & 1 \end{array} \right]


reduced row echelon form (rref)

\left[ \begin{array}{ccc|c} 1 & 0 & 0 & 2 \\ 0 & 1 & 0 & 3 \\ 0 & 0 & 1 & -1 \end{array} \right]

저작자표시 비영리 변경금지 (새창열림)