We show how to find the eigenvectors for the 3 by 3 matrix whose eigenvalues were calculated in a separate presentation.

We use the same 2 by 2 matrix whose eigenvalues were found in another MathsCast (Eigenvalues of a 2 by 2 matrix) and find the assocIated eigenvectors.

Eigenvalues of a 3 by 3 matrix are calculated. Some useful advice is given concerning factorization of the characteristic equation.

We show how to find eigenvalues for an NxN matrix then do a 2x2 example. This MathsCast follows from an introductory MathsCast on eigenvalues and eigenvectors and it is also helpful to view the presentations on linear dependence and independence first.

In this recording, addition of binary numbers is demonstrated, with reference to a specific example.

We introduce geometric series involving a combination of partial fractions derived from a quadratic denominator. It is shown how to develop series which converge for any value of x by treating the partial fractions in different ways before expansion.

We look at several examples of adding and subtracting positive and negative numbers, including examples where there are two immediately adjacent signs (e.g. two negative signs).

We look at how to factorise a number into a product of prime factors, with several examples.

Two examples are given of rearranging an equation or formula to make a particular letter the subject. This is done by first considering each operation that was originally done to the required letter, and then reversing these operations.

We look at how to find the least common multiple of two or more whole numbers, by first factorising the numbers into a product of prime numbers and then comparing the results.