 So what other elementary operations can we perform on the entries of a matrix? So let M be the augmented coefficient matrix for a system of equations. If C is some real number, can we add C to every entry of a row? Can we multiply every entry of a column by C? And can we multiply a row by a constant and add it to another row? So remember that every row corresponds to the coefficient and constant terms of one equation. So if we add C to every entry of a row, we're adding C to every coefficient and to the constant. But we can't do that in a system of equations, so this operation is forbidden. Now suppose we multiply every entry in a column by a constant C. Since every row corresponds to an equation, and every column to the coefficients of one variable in the system of equations, this corresponds to multiplying all the coefficients of a given variable by C. But we can't do that in a system of equations, and so this operation is forbidden. Finally, how about multiplying a row by a constant and adding it to another row? If we multiply every term of a row by a constant, that's just like multiplying an equation by a constant, and we're allowed to do that. If we then add these entries to another row, we're adding two equations together. And since we're allowed to do this, this operation is allowable.