Absolute Error
... This method is a variation of Gaussian elimination method. In this method, the elements above and below the diagonal are simultaneously made zero. That is a given system is reduced to an equivalent diagonal form using elementary transformations. Then the solution of the resulting diagonal system is ...
... This method is a variation of Gaussian elimination method. In this method, the elements above and below the diagonal are simultaneously made zero. That is a given system is reduced to an equivalent diagonal form using elementary transformations. Then the solution of the resulting diagonal system is ...
GEOMETRY SEMESTER EXAM-CHAPTERS 1-6
... 18) A teacher is buying supplies for two art classes. For class 1, the teacher buys 24 tubes of paint, 12 brushes, and 17 canvasses. For class 2, the teacher buys 20 tubes of paint, 14 brushes, and 15 canvasses. Each tube of paint costs #3.35, each brush costs $1.75, and each canvass costs $4.50. ...
... 18) A teacher is buying supplies for two art classes. For class 1, the teacher buys 24 tubes of paint, 12 brushes, and 17 canvasses. For class 2, the teacher buys 20 tubes of paint, 14 brushes, and 15 canvasses. Each tube of paint costs #3.35, each brush costs $1.75, and each canvass costs $4.50. ...
No Slide Title
... Unit 3 Lecture 25 Solving Equations with Algebraic Fractions Solving Equations with Fractions ...
... Unit 3 Lecture 25 Solving Equations with Algebraic Fractions Solving Equations with Fractions ...
MATH 831 HOMEWORK SOLUTIONS – ASSIGNMENT 8 Exercise
... ii): Denote the Jacobson radicals of A and B by RA and RB respectively. We need to show that RA = RB ∩ A. Choose x ∈ RB ∩ A and an arbitrary a ∈ A. Then 1 + ax ∈ A is a unit in B by Proposition 1.9 and hence is a unit in A by part i). Therefore x ∈ RA by Proposition 1.9 again. Hence RB ∩ A ⊆ RA . (Y ...
... ii): Denote the Jacobson radicals of A and B by RA and RB respectively. We need to show that RA = RB ∩ A. Choose x ∈ RB ∩ A and an arbitrary a ∈ A. Then 1 + ax ∈ A is a unit in B by Proposition 1.9 and hence is a unit in A by part i). Therefore x ∈ RA by Proposition 1.9 again. Hence RB ∩ A ⊆ RA . (Y ...
On derivatives of polynomials over finite fields through integration
... be represented as f (x) = i=0 ai xi but the coefficients ai must satisfy certain conditions, see Section 2. In [10], the properties of the set of differential functions defined as DF q = {Da F (x) : F (x) ∈ Fq [x], a ∈ F∗q } was investigated. One should notice that there exist polynomials in Fq [x] ...
... be represented as f (x) = i=0 ai xi but the coefficients ai must satisfy certain conditions, see Section 2. In [10], the properties of the set of differential functions defined as DF q = {Da F (x) : F (x) ∈ Fq [x], a ∈ F∗q } was investigated. One should notice that there exist polynomials in Fq [x] ...
Equation
In mathematics, an equation is an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions. An equation differs from an identity in that an equation is not necessarily true for all possible values of the variable.There are many types of equations, and they are found in all areas of mathematics; the techniques used to examine them differ according to their type.Algebra studies two main families of equations: polynomial equations and, among them, linear equations. Polynomial equations have the form P(X) = 0, where P is a polynomial. Linear equations have the form a(x) + b = 0, where a is a linear function and b is a vector. To solve them, one uses algorithmic or geometric techniques, coming from linear algebra or mathematical analysis. Changing the domain of a function can change the problem considerably. Algebra also studies Diophantine equations where the coefficients and solutions are integers. The techniques used are different and come from number theory. These equations are difficult in general; one often searches just to find the existence or absence of a solution, and, if they exist, to count the number of solutions.Geometry uses equations to describe geometric figures. The objective is now different, as equations are used to describe geometric properties. In this context, there are two large families of equations, Cartesian equations and parametric equations.Differential equations are equations involving one or more functions and their derivatives. They are solved by finding an expression for the function that does not involve derivatives. Differential equations are used to model real-life processes in areas such as physics, chemistry, biology, and economics.The ""="" symbol was invented by Robert Recorde (1510–1558), who considered that nothing could be more equal than parallel straight lines with the same length.