LEVEL 1

Chapter 8: Using matrices and determinants
Chapter 8: to solve equations

Solving simultaneous equations using the inverse matrix



Introduction

The power of matrix algebra is seen in the representation of a system of simultaneous linear equations as a matrix equation. Matrix algebra allows us to write the solution of the system using the inverse matrix of the coefficients. In practice, the method is suitable only for small systems. Its main use is the theoretical insight it provides into such problems.



prerequisitesPrerequisites

Before starting this Block you should:

outcomes Learning outcomes

After completing this Block you should:

  • be familiar with the basic rules of matrix algebra
  • be able to evaluate 2 x 2 and 3 x 3 determinants
  • be able to find the inverse of 2 x 2 and 3 x 3 matrices
  • be able to use the inverse matrix of coefficients to solve a system of two linear simultaneous equations
  • be able to use the inverse matrix of coefficients to solve a system of three linear simultaneous equations
  • be able to recognise and identify cases where the solution is not unique or does not exist


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