Solutions of Linear SystemsSolving a linear system involves finding the set of points that simultaneously satisfy all the equations of the system. To find this set, represent the system as an augmented matrix, and then apply elementary row operations to reduce the system to either upper triangular form (Gaussian elimination) or diagonal form (Gauss-Jordan elimination). Once the system has been reduced, the solution is obtained by solving for the unknown terms from the bottom up (the "back substitution" step).

You can use interactive commands for each of the two elimination methods, and an interactive command that allows you to solve a linear system.

The commands produce maplets, which are dialogs that present the current state of the problem and request your next step. You can, for example, apply an elementary row operation, request a hint, go back a step, or request the solution. After each computation, the previous and current states of the matrix are displayed, as well as a text description of the recently applied step.

If the input to GaussianEliminationTutor or GaussJordanEliminationTutor is a Matrix, then when the reduction work is completed, a maplet is displayed. Using this maplet, you can request information about the rank, nullity, row space, column space, and null space of the matrix.> If the input is a Matrix and a Vector, then when the reduction work is completed, a maplet is displayed. Using this maplet, you can complete the solution of the corresponding linear system.> More generally, you can use the LinearSolveTutor maplet to solve linear systems. For this command, you can provide the input problem either as a Matrix and Vector, where the Vector represents the right-hand side values, or as an augmented Matrix, where the right-hand side values are taken from the last column of the Matrix.

You must select whether to solve the problem using Gaussian elimination or Gauss-Jordan elimination.>