CAIE 9231 Further Mathematics Matrix II review notes Paper 2: Further Pure Mathematics 2

Candidates should be able to:
• formulate a problem involving the solution of
3 linear simultaneous equations in 3 unknowns
as a problem involving the solution of a matrix
equation, or vice versa

• understand the cases that may arise concerning
the consistency or inconsistency of 3 linear
simultaneous equations, relate them to the
singularity or otherwise of the corresponding
matrix, solve consistent systems, and interpret
geometrically in terms of lines and planes

• understand the terms ‘characteristic equation’,
‘eigenvalue’ and ‘eigenvector’, as applied to
square matrices

• find eigenvalues and eigenvectors of 2 × 2 and
3 × 3 matrices
Restricted to cases where the eigenvalues are real
and distinct.
• express a square matrix in the form QDQ–1,
where D is a diagonal matrix of eigenvalues and
Q is a matrix whose columns are eigenvectors,
and use this expression

• use the fact that a square matrix satisfies its own
characteristic equation.