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Echelon Forms

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For each of the following matrices choose which are:

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a) In row echelon form but not in reduced row echelon form.

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b) In reduced row echelon form.

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c) Neither a) nor b).

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Choose which of 5 matrices are in a) row echelon form but not reduced b) reduced row echelon form c) neither.

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A matrix is in row echelon form if:

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- all nonzero rows (rows with at least one nonzero element) are above any rows of all zeroes (all zero rows, if any, belong at the bottom of the matrix)

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- the leading coefficient (the first nonzero number from the left) of a nonzero row is always strictly to the right of the leading coefficient of the row above it (thus all entries in a column below a leading coefficient are zeros)

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- the leading entry of each nonzero row is always 1 (called a leading 1)

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A matrix is in reduced row echelon form if the above are all true, but also

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-each column containing a leading 1 has zeros everywhere else

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We can use these definitions to determine which matrices are in row echelon and reduced row echelon form.

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