Also note that most teachers will probably think that adding extra rows and columns of zeros to a matrix is a mistake (and it is if you dont know why it is ok). Matrix, the one with numbers, arranged with rows and columns, is extremely useful in most scientific fields. Note that your equation never had any solutions from the start, as the RRE indicates on the second row: 0 -2/3. The value for x can be derived in a similar manner. This is the RRE form of your augmented matrix. Y = D y D = | a 1 c 1 a 2 c 2 | | a 1 b 1 a 2 b 2 | = a 1 c 2 − a 2 c 1 a 1 b 2 − a 2 b 1 And the numerator is the determinant of the matrix formed by replacing the column that represents the coefficients of y with the corresponding column of constants. The denominator is the determinant of the coefficient matrix. The adjugate matrix is noted as Adj(M).Both the numerator and denominator look very much like a determinant of a 2×2 matrix. This is sometimes referred to as the adjoint matrix.
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