product matrix equation - American Mathematical Society
... \-matrix which has an inverse which is also a X-matrix is called unimodular. If TA =B where T, A, and B are X-matrices and T is unimodular, then A is said to be a left associate of B. Every square X-matrix is the left associate of a unique X-matrix of the following form: Every element below the main ...
... \-matrix which has an inverse which is also a X-matrix is called unimodular. If TA =B where T, A, and B are X-matrices and T is unimodular, then A is said to be a left associate of B. Every square X-matrix is the left associate of a unique X-matrix of the following form: Every element below the main ...
Number Theory Week 9
... The corresponding elements of Z105 are found by using the same method as used in the example given in Lecture 16. For example, the element x ∈ Z105 such that x ≡ 2 (mod 3), x ≡ 1 (mod 5) and x ≡ 5 (mod 7) is 26. The other two solutions of x3 = 41 are 94 (corresponding to (2,1,3)) and 41 (correspondi ...
... The corresponding elements of Z105 are found by using the same method as used in the example given in Lecture 16. For example, the element x ∈ Z105 such that x ≡ 2 (mod 3), x ≡ 1 (mod 5) and x ≡ 5 (mod 7) is 26. The other two solutions of x3 = 41 are 94 (corresponding to (2,1,3)) and 41 (correspondi ...
Discuss on Equations of Lines
... Equations involving one or two variables can be graphed on any x− y coordinate plane. In general, the following principles are true: ...
... Equations involving one or two variables can be graphed on any x− y coordinate plane. In general, the following principles are true: ...
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.