This topic could be placed in a number of mathematical categories (numbers, linear algebra, matrices, calculus, and others).

I toyed with listing it in the [Algebra] section of this website, because determinants were first created as a method for rapidly solving simultaneous linear equations. Once mathematicans realised that they were really numbers, however, they became curious about their properties … how to add, subtract, multiply and divide them (and more). So, that is why you find them here, among the numbers.

You can see, from the illustration to the left, that the determinant of the 2×2 matrix (represented with parentheses) is written using the same array of numbers with a vertical line on either side. For a 2×2 matrix, the determinant is *calculated* (evaluated) by multiplying the numbers on the leading diagonal (3)(7) and subtracting the product of the remaining numbers on the other diagonal (5)(-1). As you can see, this results in a single number.

Why are they used, what are they useful for, and how they are manipulated will be revealed on this page in time. I will also be sharing about the history of linear equations, matrices and determinants.

I was going to provide a link to a useful site for you to use in the meantime, but I cannot find a site that starts from the basic properties of an array of linear equations. I believe in starting with such an array and then deducing the concepts of matrix multiplication, inverse matrices, transposed matrices, and determinants. Please be patient.

From the beginning of my schooling I had struggled with Mathematics. Highly discouraged by my results, I grew to eventually hate Maths and lost all motivation to improve. Then part way through year seven my parents decided to send me to Crystal Clear Mathematics. Graeme was able to quickly identify areas I needed to improve and explain Maths in a way that finally made sense to me. I was able to understand Maths. This in turn then affected my confidence in my own ability.

Since working with Graeme I have gone from failing to significantly improved results. I now get As & Bs both in examinations and for assignment tasks. Graeme is patient, kind and his tutoring is individualised. He was so helpful and I am grateful for his help.

Tessa M (student, 2014-2017)

See all Testimonials