The first augmented matrix is in Row echelon form
The second augmented matrix is in reduced row-echelon form
The third augmented matrix is neither row echelon nor reduced.
What is echelon form?
Echelon form means that the matrix is in one of two states:
- Row echelon form.
- Reduced row echelon form.
This means that the matrix meets the following three requirements:
The first number in the row (called a leading coefficient) is 1. Note: some authors don’t require that the leading coefficient is a 1; it could be any number. You may want to check with your instructor to see which version of this rule they are adhering to).Every leading 1 is to the right of the one above it.Any non-zero rows are always above rows with all zeros.
So matrix
[tex]\left[\begin{array}{ccc}4&11&2\\0&-5&8\\0&0&-2\end{array}\right] \left[\begin{array}{c}-6&7&3\end{array}\right][/tex]
The above matrix is in row echelon form
[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] \left[\begin{array}{c}-6&3&3\end{array}\right][/tex]
The above matrix is in Reduced echelon form
[tex]\left[\begin{array}{ccc}1&0&3\\0&6&0\\7&0&1\end{array}\right] \left[\begin{array}{c}-6&8&13\end{array}\right][/tex]
The above matrix is neither row-echelon nor reduced row echelon matrix.
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