Question

Backward substitution is carried out in echelon / reduced-echelon form.

Answer 1

Reduced Echelon form

Explanation:

In Echelon form, the lower left triangle is all zeros and the diagonal from top left to bottom right of the "square" portion of the matrix is all 1s. But the upper right triangle could be any real number.

In Reduced Echelon form, the square portion of the matrix is all zeros except across the diagonal. This allows a person to identify the values of x₁, x₂, x₃, and so forth just by looking at the matrix, instead of having to do the back substitution.