Conclusion

Following completion of this free OpenLearn course, Introduction to linear equations and matrices, as well as being able to understand ‘the basics of using matrices to represent systems of linear equations’ you should also find that your skills in producing convincing arguments and problem solving are improving.

You should now be able to:

• use the method of Gauss-Jordan elimination to find the solutions of systems of simultaneous linear equations
• solve a system of linear equations by row-reducing its augmented form
• perform the matrix operations of addition, multiplication and transposition and express a system of simultaneous linear equations in matrix form
• determine whether or not a given matrix is invertible and if it is, find its inverse
• evaluate the determinant of a 2 x 2 or 3 x 3 matrix and use the determinant to determine whether or not a given 2 x 2 matrix is invertible.

This free OpenLearn course is an extract from the Open University course M208 Pure mathematics [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] .

If you feel you are ready to move on in your study of pure mathematics but don’t have time to study a full Open University course at this time, you might like to study the free OpenLearn courses Introduction to group theory and Introduction to analysis. They are further adapted extracts from the Open University course M208 Pure mathematics.

Alternatively, if you are interested in applied mathematics, you might like to try the free OpenLearn courses Second-order differential equations and Dynamics. If you are interested in statistics, you might like to try the free OpenLearn courses Modelling and estimation, Medical statistics and Bayesian statistics.