In which case, I suspect the rotations I need to use are the ones which simply switch two rows ( since we're left multiplying by the rotation matrices; the matrices I'm referring to are the ones corresponding to the elementary row operation of row-switching ).
12.
A matrix is said to be in "'reduced row echelon form "'if furthermore all of the leading coefficients are equal to 1 ( which can be achieved by using the elementary row operation of type 2 ), and in every column containing a leading coefficient, all of the other entries in that column are zero ( which can be achieved by using elementary row operations of type 3 ).
13.
A matrix is said to be in "'reduced row echelon form "'if furthermore all of the leading coefficients are equal to 1 ( which can be achieved by using the elementary row operation of type 2 ), and in every column containing a leading coefficient, all of the other entries in that column are zero ( which can be achieved by using elementary row operations of type 3 ).
