Given the matrices A 0 1 0 0 0 0 1 0 0 0 2 0 B 2 0 1 3 0 1

Given the matrices: A = [0 1 0 0 0 0 1 0 0 0 2 0], B = [2 0 1 3 0 -1 1 4 0 0 0 1], C = [1 0 0 0 0 1 1 2 0 0 0 0], D = [0 1 0 0 1 0 2 1], E = [1 0 2 1 0 1 3 4 0 0 1 0] F = [1 2 -1 4 0 1 0 3 0 0 1 -2], G = [1 2 -1 2 0 0 0 0 0 1 2 4], H = [1 3 -5 0 0 1 0 0 1] (a) Determine the matrices that are in Row-Echelon Form. (b) Determine the matrices that are in Reduced Row-Echelon Form.

Solution

Answer

Row echelon form :

A matrix is in row echelon form if it meets the following requirements:

The first non-zero number from the left (the “leading coefficient”) is always to the right of the first non-zero number in the row above.

Rows consisting of all zeros are at the bottom of the matrix.

Reduced row echelon form :

A matrix is in row echelon form (ref) when it satisfies the following conditions.

The first non-zero element in each row, called the leading entry, is 1.

Each leading entry is in a column to the right of the leading entry in the previous row.

Conclusions :

A is not in reduced row echelon form and not in row echelon form

B is in row echelon form but not in reduced row echelon form

C is both in reduced row echelon form and in row echelon form

D is not in reduced row echelon form and not in row echelon form

E is both in reduced row echelon form and in row echelon form

F is both in reduced row echelon form and in row echelon form

G  is not in reduced row echelon form and not in row echelon form

H  is not in reduced row echelon form and not in row echelon form