Math 1313 Section 3.2 Section 3.2: Solving Systems of Linear Equations Using Matrices As you may recall from College Algebra or Section 1.3, you can solve a system of linear equations in two variables easily by applying the substitution or addition method. Since these methods become tedious when solving a large system of equations, a suitable technique for solving such systems of linear equations will consist of Row Operations. The sequence of operations on a system of linear equations are referred to equivalent systems, which have the same solution set. Row Operations 1. Interchange any two rows. −53131221RR↔−3125312. Replace any row by a nonzero constant multiple of itself. −−8243122241RR→−−22113123. Replace any row by the sum of that row and a constant multiple of any other row. −312531221RRR2→+−−−770531Row Reduced Form An m x n augmented matrix is in row-reduced form if it satisfies the following conditions: 1. Each row consisting entirely of zeros lies below any other row having nonzero entries. −−210000301the correct row-reduced form −−0002103012. The first nonzero entry in each row is 1 (called a leading 1).