Mat 1332a, fall2018: reduce the following matrix to rref: 2x1 x1 x2 + x3 = 2, x1 + x2. + x3 = 5: determine whether each of the following systems of linear equations has no solution, or it has a unique solution, or it has infinitely many solutions. If a system is consistent, solve the system to find the solution. If a system has infinitely many solutions, express the general solution in the parametric form. (i) (ii) (iii) 2x1 x2 + x3 = 2, x1 + 2x2 + 3x3 = 1, x1 3x2 x3 = 3. Solution. x1 + 2x2 + 3x3 = 5, The general solution is x3 = t, x2 = 1 / 2 + (1 / 2)t, x1 = 2 + x2 t = (5 / 2) (1 / 2) t. (ii) This system has a unique solution: x3 = 2, x2 = 3x3 7 = 1, x1 = 2x2 3x3 + 5 = 1. (iii)
