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April 29, 2022


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In this course, matrices are used as a concise way of representing systems of linear equations which occur frequently in mathematics.

Section 1 looks at simultaneous linear equations in two and three unknowns and then generalises the ideas to systems of linear equations. Section 2 develops a strategy for solving systems of linear equations. Section 3 looks at the algebra of matrices and shows that matrices can be thought of as a generalisation of vectors. Section 4 introduces the inverse of a matrix. Section 5 uses systems of linear equations to introduce the determinant of a square matrix.

Course learning outcomes

After studying this course, you should 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.

Course Curriculum

  • Introduction 00:25:00
  • Learning outcomes 00:10:00
  • Link to course PDF 00:30:00
  • Conclusion 00:15:00

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Open University UK