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Matrix Echelon Form

Echelon Form

A matrix is in echelon form if nonzero rows appear above the zero rows, nonzero rows' first nonzero element is a leading one, leading ones in upper rows appears to the left of the leading ones in any lower rows.

Row Reduced Echelon Form

A matrix is in row reduced echelon form if nonzero rows appear above the zero rows, nonzero rows' first nonzero element is a leading one, leading ones in upper rows appears to the left of the leading ones in any lower rows, all elements in the column above and below a leading one are zero.

Examples

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  • Find the echelon form of the matrix $$\begin{pmatrix}1&2\\3&4\end{pmatrix}+\begin{pmatrix}1&2\\3&4\end{pmatrix}$$
  • Find the row reduced echelon form of the matrix $$\begin{pmatrix}1&2\\3&4\end{pmatrix}+\begin{pmatrix}1&2\\3&4\end{pmatrix}$$