Question

1. Make your own example of a 5-by-3 matrix that is in echelon row but do not reduce row echelon form.

2. Repeat for a 2-by-6 matrix

3. Make a 4-by-4 rref matrix whose first column contains only zeros

Answer 1

a matrix is in row echelon form if

• 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), and
• the leading coefficient (the first nonzero number from the left, also called the pivot) of a nonzero row is always strictly to the right of the leading coefficient of the row above it

1.

2.

3.

Reduced row echelon form is a type of matrix used to solve systems of linear equations. Reduced row echelon form has four requirements:

• The first non-zero number in the first row (the leading entry) is the number 1.
• The second row also starts with the number 1, which is further to the right than the leading entry in the first row. For every subsequent row, the number 1 must be further to the right.
• The leading entry in each row must be the only non-zero number in its column.
• Any non-zero rows are placed at the bottom of the matrix.