Proof by contradiction (also known as indirect proof or the method of reductio ad absurdum) is a

Absolute value equalities and inequalities are equalities and inequalities in which the unknown or

For the given vector space $V$, we want more study the space $L (V, \mathbb{F})$, where $\mathbb{F}$

In this lesson we will examine in detail the procedure of joining the matrices to the vectors and

Definition. Let $V$ and $W$ be two vector spaces over the same field $\mathbb{F}$. A transformation

Let $$p(x) = ax^2 + bx + c,  \quad a \neq 0$$ be the second degree polynomial. We can factorize it

Absolute value of a number represents its distance from zero on a number line. Since it represents a

Definition. Let $V$ be a vector space over the field $\mathbb{F}$. Any vector $v$ of the form $$v =

Euler’s phi function For arbitrarily chosen natural number $m$, we observe the following

A non- linear Diophantine equation is every Diophantine equation which is not linear. For instance,

Let $f$ be a polynomial with integer coefficients in one or more variables. An algebraic equation of

For every two nonnegative real numbers $a$ and $b$ the following inequality holds: $$ \frac{a+b}{2}

Let $a_{3}x^{3}+a_{2}x^{2}+a_{1}x+a_{0}=0$, $a_{3}\neq 0$ be the cubic equation. By dividing the

Example 1. For a matrix $$\mathbf{A} = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$$ find

Linear system of equations Regarding the introduction of matrices, we can find their connection with

Determinant of a matrix The determinant is a real function  such that each square matrix

Regular matrix A square matrix $\mathbf{A}$ of order $n$ is a regular (invertible) matrix if exists

Addition of matrices To define the addition of two matrices $\mathbf{A}=[a_{ij}]$ and

Let $n$ and $m$ be natural numbers. Every rectangular array $\mathbf{A} =  \begin{bmatrix}  a_{11}

Operations are divided into three degrees, exponents and roots, multiplication and division, addition ...

Function is injection if the equality of function values implies the equality of arguments.

The binomial theorem, also known as binomial expansion, explains the expansion of powers.

Here we’ll explain the method for rough sketching of polynomials.

Number of positive real roots of a polynomial is bounded by the number of changes of sign in its

The Irrational Root Theorem says if a + √b is also a root of observed polynomial.

The Rational Root Theorem says if a polynomial equation a_n x^n + ... + a0 = 0

If a polynomial equation a_n x^n + + ... + a_0 = 0 has an integer solution, a is not equal to 0

Polynomial equations are special type of equations that come in the one different form...

Factoring is an action where polynomial is represented as a product of simpler polynomials that no

Fundamental theorem of algebra says every polynomial with degree n ≥ 1 has exactly n zeros...

Radical equations are equations in which the unknown appears under a radical sign.

The problem of solving quadratic inequalities is very much connected to solving zeros.

One of the most important basics in theory of number is the definition of divisibility with rules.

Solve both of your inequalities individually and search for the intersection of their common solution

Vectors are directed line segments in which we can make difference between initial and terminal point.

Radicals is created with an opposite action from exponentiation. They are marked with specific symbol.

Polynomial is an expression consisting of variables and coefficients. It's made out of one or more terms.

Exponent is a number which tells us how many times a number has been multiplied by itself.

A linear function has a correspondence between two sets - one element is assigned to element.

They are similar to any other type of inequalities. The only difference is their absolute value.

Compound inequalities are a little bit more complicated... They are bounded by more than one condition.

The most difficult type of inequalities to solve. It includes operations with integers, decimals and

Inequalities that can be solved in maximum two steps are known as two-step inequalities.

The simplest form of inequalities are known as one-step inequalities. It can be solved in one step.

Inequalities represent relations between two objects. There are one-step, two-step and multi-step.

Quadratic equation are type of equations that have exactly two solutions (ax2 + bx + c = 0, a ≠ 0)

Find the unknown numbers in two or more linear equations using graphing, elimination or substitution.

More complex equations. Equations that needs to be solved in more than two steps.

Two-step equations are simple equations in which solution can be found in just two steps.

The simplest equations that require only one basic operation to find the solution.