Further MathematicsCode 9231
Matrices
What this topic asks you to be able to do
- translate a situation needing 3 linear simultaneous equations in 3 unknowns to be solved into one needing a matrix equation to be solved, or the reverse
- understand the possible situations regarding whether 3 linear simultaneous equations are consistent or inconsistent, link these to whether the associated matrix is singular or not, solve the consistent systems, and describe each situation geometrically using lines and planes
- understand what is meant by the words ‘characteristic equation’, ‘eigenvalue’ and ‘eigenvector’ when they relate to square matrices
- find the eigenvalues and the eigenvectors of any 2 × 2 or 3 × 3 matrix
- express a square matrix as QDQ–1, where D is diagonal and contains the eigenvalues while the columns of Q are eigenvectors, then apply that expression
- apply the result that every square matrix obeys its own characteristic equation