For a given set of m linear equations in n unknowns x1, x2,…xn,
a11x1 + a12x2 + ⋯ + a1nxn = b1,
a21x1 + a22x2 + ⋯ + a2nxn = b2,
am1x1 + am2x2 + ⋯ + amnxn = bm,
the augmented matrix is the matrixobtained by adjoining to the matrix of coefficients an extra column of entries taken from the right-hand sides of the equations. The solutions of a set of linear equations may be investigated by transforming the augmented matrix to echelon form or reduced echelon form by elementary row operations. See Gaussian elimination; Gauss-Jordan elimination.