Backward substitution can be carried out in both echelon and reduced row echelon forms, True.
How is Backward substitution carried out?
Backward substitution is typically carried out in the context of solving a system of linear equations that has been transformed into upper triangular form, which is a characteristic of either echelon form (also known as row echelon form) or reduced row echelon form (also known as row reduced echelon form).
Echelon Form (Row Echelon Form):
In this form, all nonzero rows are above any rows of all zeroes.
Each leading entry (the first nonzero number from the left, also known as a pivot) in a row is to the right of the leading entry in the previous row.
All entries in the column below a leading entry are zeros.
Reduced Row Echelon Form (Row Reduced Echelon Form):
This form has all the properties of the echelon form.
Additionally, the leading entry in each nonzero row is 1, and it is the only nonzero entry in its column.
Backward substitution is particularly straightforward in systems that are in reduced row echelon form, as each equation can be solved for one variable at a time, starting from the bottom row and working upward.
Complete question:
Backward substitution is carried out in echelon / reduced-echelon form. T/F?