Determine which matrices are in reduced echelon form and which others are only i

Question

Determine which matrices are in reduced echelon form and which others are only in echelon form.

matrix 1

1 0 0 0
0 2 0 0
0 0 1 1

matrix2

1 0 0 0
0 1 0 0
0 0 1 1

matrix 3

0 0 0 0
1 6 0 0
0 0 1 0
0 0 0 1

Is matrix a in reduced echelon form, echelon form only, or neither?
echelon form onlyechelon form only
reduced echelon formreduced echelon form
neither

Is matrix b in reduced echelon form, echelon form only, or neither?
echelon form onlyechelon form only
reduced echelon formreduced echelon form
neither

Is matrix c in reduced echelon form, echelon form only, or neither?
reduced echelon form
echelon form only
neither

Explanation / Answer

Specifically, a matrix is in row echelon form if

A matrix is in reduced row echelon form (also called row canonical form) if it satisfies the following conditions:

matrix 1

1 0 0 0
0 2 0 0
0 0 1 1

Echelon form: Yes {no zero row, all the leading coefficient strictly to the right of the above one}

Reduced row echelon form: No {2nd row leading coefficient is not 1}

matrix2

1 0 0 0
0 1 0 0
0 0 1 1

Echelon form: Yes {no zero row, all the leading coefficient strictly to the right of the above one}

Reduced row echelon form: Yes {leading coefficients are 1}

matrix 3

0 0 0 0
1 6 0 0
0 0 1 0
0 0 0 1

Echelon form: No {zero row on the top}

Reduced row echelon form: No {not echelon form}

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