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Linear-Algebra · Row-Reduction

Rref [[1,2,3],[4,5,6]]

\left[\begin{matrix}1 & 2 & 3\\4 & 5 & 6\end{matrix}\right]

Gawo ndi Gawo

  1. \left[\begin{matrix}1 & 2 & 3\\4 & 5 & 6\end{matrix}\right]

    Gauss-Jordan elimination.

  2. \left[\begin{matrix}1 & 2 & 3\\0 & -3 & -6\end{matrix}\right]

    R2 ← R2 − (4)·R1 to clear column 1.

  3. \left[\begin{matrix}1 & 2 & 3\\0 & 1 & 2\end{matrix}\right]

    R2 ← R2 / -3 to make the pivot 1.

  4. \left[\begin{matrix}1 & 0 & -1\\0 & 1 & 2\end{matrix}\right]

    R1 ← R1 − (2)·R2 to clear column 2.

  5. \left[\begin{matrix}1 & 0 & -1\\0 & 1 & 2\end{matrix}\right]

    Reduced row-echelon form.

Kusonyeza yankho
\left[\begin{matrix}1 & 0 & -1\\0 & 1 & 2\end{matrix}\right]