 Hi everyone, it's MJ and welcome to this introduction video on linear algebra. And we're going to start with a quote coming from a book by Benjamin Perce called Linear Associative Algebra written in 1882. An entity says that mathematics is the science which draws necessary conclusions. The words of common language are usually unfit for mathematics and so symbols must be adopted. The mathematics treated by such symbols is called algebra. Algebra then is formal mathematics. So let's look at algebra. It is the study of structures and it is a foundational branch of mathematics that you most likely covered at school and it's a very general term. What we're going to be doing in these videos is looking at linear algebra which means we're going to be studying linear structures. So for example we've got some linear equations. They normally written the form ax plus b equals zero or linear maps such as the function of x is equal to y. But now what we can do is we can represent these linear equations and linear maps using vectors and matrices. Now why do we do this? Well because it will aid with the computation of many other areas of maths. Not only just geometry but a lot of applied topics such as engineering, computer science, actuarial science etc. So very quick history. It kind of all started with Eulud in an ancient Greek, ancient Greece where he kind of saw that reality is made up of three dimensions of space. Then in the 17th century we have Rene Descartes who said you know what we can reduce geometric problems to algebraic computations and that was very very a very big idea to to make. And then we'll see from Leipniz to more recently Piano where we formalize the the whole study of linear algebra. So if we had a look at linear algebra we also need to ask ourselves well why do actuaries need it? And I guess the quick answer is to say well it makes complex computations easier and we do see it popping up in many of our different exams. So that's just financial engineering, survival models, enterprise risk management and a lot more. In fact I'm going to give you a quick little sneak peek of some of the things that use matrices in actuarial science. So we're not going to go into this right now because in these videos we're just going to be covering the basics. So coming up in the series we're going to be looking at vectors and vector operations. We're going to be looking at matrices and their operations as well as what you know what are determinants and inverse matrices. We're then going to look at how we can solve simultaneous equations and we're going to end off with eigenvalues and eigenvectors. So yeah looking forward to the rest of the videos in the series on linear algebra.