⇒ You can use the inverse of a 3 x 3 matrix to solve a system of three simultaneous linear equations in three unknowns

⇒ You need to be able to determine whether a system of three linear equations in three unknowns is consistent or inconsistent

⇒ A system of linear equations is consistent if there is at least one set of values that satisfies all the equations simultaneously. Otherwise, it is inconsistent

⇒ If the matrix corresponding to a set of linear equations is non-singular, then the system has one unique solution and is consistent. However, if the matrix is singular, there are two possibilities: either the system is consistent and has infinitely many solutions, or it is inconsistent and has no solutions

⇒ You can visualise the different situations by conidering the points of intersection of the planes corresponding to each equation. Here are some of the different possible configurations:

⇒ Also see our notes on:

• Introduction to Matrices
• Matrix Multiplication
• Determinants
• Inverting a 2 x 2 Matrix
• Inverting a 3 x 3 Matrix