In previous sections we’ve talked about Gauss elimination method and considered some examples. Today we have one more systems of linear equations to solve, but this time we’ll apply matrix representation for systems of linear equations:
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Gauss elimination method tutorial
If you need to solve a system of linear equations, Gaussian elimination is often the best choice. We’ve considered this topic in one of the previous sections. For better understanding we prepared several examples covering this topic similar to those in linear algebra homework. Now let’s solve the system of 3 linear equations with 3 unknowns (more…)
How to comb a hairy ball
Have you ever tried to comb a hairy ball? Really, it is a very important and responsible work. It roots back to old 1912. A Holland mathematician Luitzen Brouwer, who worked in a field of topology and set theory, had shown that hairy ball cannot be brushed in such a way to be smooth and without intersections of hairsprings. At least one hairspring should stick up. This result is now called a hairy ball theorem. (more…)
Gaussian elimination method for solving systems of linear algebraic equations
What do you know about solving systems of linear equations? This type of tasks is often offered to students in linear algebra homework. In one of our videos we discussed that a system of linear equations can be solved using Cramer’s rule which involves finding determinants and it might get tricky when dealing with systems of 4, 5 or more equations. Luckily, there is another method which allows to avoid massive calculations. And it is called Gaussian elimination (or row reduction). (more…)
Inverse matrix
Inverse matrices are widely applied. For example, suppose you’re asked to perform matrix division in your linear algebra homework. As we said in one of previos articles about basic matrix operations, matrix division is in fact multiplication by an inverse matrix. If you are going to solve a system of equations in matrix representation you’ll also need to find inverse matrix. So let’s talk about inverse matrices and how to find them. (more…)
Why Java is the best choice
If you’re studying computer science you’ve probably already have completed a lot of programming homework, including Java, or it’s just around the corner. If you don’t, well, sure you’re also using Java codes in everyday life, not even having the faintest clue about that. Ok, let us start with some history.
Java was first introduced in 1995 year by the “Sun Microsystems” company. Java programming language is considered to be a c++ “child”. Its main advantage is that it does not “bind” itself to any operating system.
Java source code is translated to special byte code, translatable by a virtual machine on any operating system. Such languages are called cross-platform languages. Java is considered to be most popular because of it’s wide implementable and cross-platform supported. (more…)
Why gold foil is on space objects?
You could notice that many NASA photographs of spacecraft often feature items wrapped in golden foil. Obviously, it is used for insulation. But why NASA uses gold? And how does it work? As it is known, in space there is solar radiation, which affects the Earth’s atmosphere and is the main source of energy for all the processes in nature. (more…)
