Math - Page 8

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).  Continue reading →

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. Continue reading →

Do you know what is a determinant? A determinant of a matrix is a special number which is defined only for square matrix. It can be calculated in several ways, today we’ll introduce one of them which is called Laplace expansion.

Why do we need determinants? Basically, the determinant can tell us a lot of useful things about matrix, it’s helpful when finding the inverse matrix and solving systems of linear equations (recall Cramer’s rule) and so on. Continue reading →

Having difficulties with matrix problems while doing math homework? In such situation it’s a great idea to ask your math tutor for help because any misunderstanding at the start can result in greater problems at your midterm and final.  Yet another great idea is to go through tutorials on the topic to straighten your knowledge on the matter. We prepared the series of articles and video tutorials covering basic concepts, also we considered several examples on matrices, similar to those in your homework, more serious assignments and exam tasks. We’ll explain how matrices are used in general, which operations are allowed to perform with matrices and how to calculate the determinants. Let’s get started. Continue reading →

The original (ancient) formulation arises from the story about how Epimenides, a native of the island of Crete, in the heat of an argument said: “All Cretans are liars”. And he heard the objection: “But you yourself are Cretan! So are you lying or not?”

If we assume that Epimenides was telling the truth, then it turns out that he like all the Cretans is a liar. Therefore he lied. If he lied, then it turns out that he, like all the Cretans, is not a liar. Then he told the truth.

Continue reading →

A series is an infinite addition of an ordered set of terms. The infinite series often contain an infinite number of terms and its nth term represents the nth term of a sequence. A series contain terms whose order matters a lot. If the terms of a rather conditionally convergent series are suitably arranged, the series may be made to converge to any desirable value or even to diverge according to the Riemann series theorem. Let the terms in a series be denoted by the symbol, a_{n ,} and the nth partial summation be denoted using the following sigma notation for any natural number n:

Continue reading →

The objects commonly referred to as platonic solids are regular solids or better still, they are called regular polyhedra. The solids are convex polyhedra that have equivalent faces made up of regular polygons that are congruent-the word polyhedra means ‘’many faces’’ in Greek. There are exactly five of the platonic solids called polyhedra and they are:

Continue reading →