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# Topic: System of linear equations

###### In the News (Wed 22 May 13)

 PlanetMath: finite-dimensional linear problem The equation is called under-determined or over-determined depending on whether the former is greater than the latter, or vice versa. This is unfortunate, because the concept of a linear equation is much more general than the traditional notion of “variables and equations”, and relies in an essential way on the idea of a linear mapping. Polynomial interpolation is a linear problem, but one that is specified abstractly, rather than in terms of variables and equations. planetmath.org /encyclopedia/SystemOfLinearEquations.html   (0 words)

 Linear Equations Worksheets, Systems of Linear Equations Worksheets, and Inequalities Worksheets. Linear Equations Worksheets, Systems of Linear Equations Worksheets, and Inequalities Worksheets. Inequalities - Sketch the graph of the inequality Linear Systems - Solve by using the substitution method (in Ax + By = C format) Crossword Puzzle www.edhelper.com /LinearEquations.htm   (569 words)

 Egwald Mathematics — Geometry, Linear Algebra, Optimal Control, Statistics and Econometrics, Nonlinear Dynamics, ... Use the "normal equations" and singular value decomposition methods to obtain the least squares solution to overdetermined systems of equations. By applying Pontryagin's Maximum Principle to the nonlinear system of equations of motion of the scud missile and shoulder mounted rocket, I derive the optimal control theory minimum time solution to intercepting the scud missile. A differential equation system with a first integral is called a conservative system. www.egwald.com /mathematics   (0 words)

 Solving a system of linear equations - The Code Project - C# Samples It is a Windows application enabling the user to set nine coefficients of three linear equations and a vector of constants and then to find the solution. The method of solution also requires calculating the determinant value of three matrices that were obtained from the "main" system matrix by an interchange of one of its columns by the vector of right-hand side. The main attention was brought to two supporting classes that were able to both keep the equation system and solve it. www.codeproject.com /cs/samples/LinearEquationsSystemSoln.asp   (0 words)

 Review from MAA Monthly of Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach Because of limitations of html, mathematical equations are omitted. The notion of derivative is introduced in terms of linear approximation... The fundamental algorithm for solving systems of linear equations is row reduction, presented in a modern fashion in terms of multiplication by elementary matrices. matrixeditions.com /VC.MAAreview.html   (1760 words)

 Systems of Linear Equations: Definitions A "system" of equations is a set or collection of equations that you deal with all together at once. Linear equations (ones that graph as straight lines) are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables. A solution for a system of equations is any point that lies on each line in the system. www.purplemath.com /modules/systlin1.htm   (442 words)

 Method for solving a large sparse triangular system of linear equations - Patent 6694343   (Site not responding. Last check: ) Thus, the system of linear equations, in matrix form, given by 100 can be rewritten, as in 102, in terms of the matrix or array representative of x, wherein the matrix given by 112 is the inverse of A, denoted A.sup.-1. Therefore, there is a need for a system which overcomes the shortcomings of prior methods (that perform more than necessary computations) and utilizes only the non-zero components of a matrix to solve large sparse triangular linear equations and generate explicitly only the non-zero entries of the solution. A system of linear equations Ax=b has to be solved where A is a very large sparse triangular matrix of order n.times.n, b is a sparse n-vector, and x is the n-vector that has to be calculated. www.freepatentsonline.com /6694343.html   (3596 words)

 Linear Inequalities and Linear Equations The output of this algorithm is a linear equation in one unknown. This equation may be solved for that unknown, and the solution may be substituted in one of the original equations yielding the value of the other unknown. of the system of n linear equations in the system of n unknown. www.personal.kent.edu /~rmuhamma/Algorithms/MyAlgorithms/MathAlgor/linear.html   (1390 words)

 Linear equation Summary   (Site not responding. Last check: ) The basic method for solving a system of linear equations is to replace a system by a new system that has the same solution set but that is easier to solve. Homogeneous systems of linear equations are ones in which all of the constant terms are zero, that is all of the bs are zero. Because of the linear property above, the solutions of linear equations of this kind can in general be described as a superposition of other solutions of the same equation. www.bookrags.com /Linear_equation   (1411 words)

 System of linear equations Summary   (Site not responding. Last check: ) Systems of equations have played an important part in the development of business and quicker methods for solutions continue to be explored. A linear equation in three variables could be represented by the equation ax + by + cz = k, where a, b, c, and k are constants and x, y, and z are variables. Systems of linear equations belong to the oldest problems in mathematics and they have many applications, such as in digital signal processing, estimation, forecasting and generally in linear programming and in the approximation of non-linear problems in numerical analysis. www.bookrags.com /System_of_linear_equations   (2347 words)

 Solving Systems of Linear Equations; Row Reduction   (Site not responding. Last check: ) Systems of linear equations arise in all sorts of applications in many different fields of study. When a sequence of elementary row operations is performed on an augmented matrix, the linear system that corresponds to the resulting augmented matrix is equivalent to the original system. Our strategy in solving linear systems, therefore, is to take an augmented matrix for a system and carry it by means of elementary row operations to an equivalent augmented matrix from which the solutions of the system are easily obtained. kahuna.sdsu.edu /~impellus/312/System.htm   (659 words)

 Egwald Mathematics — Geometry, Linear Algebra, Optimal Control, Statistics and Econometrics, Nonlinear Dynamics, ... Use the "normal equations" and singular value decomposition methods to obtain the least squares solution to overdetermined systems of equations. Solve systems of linear differential equations, using the linear algebra from the preceeding pages. A differential equation system with a first integral is called a conservative system. www.egwald.ca /mathematics   (1473 words)

 Solving Systems of Linear Equations - HMC Calculus Tutorial Systems of linear equations arise in all sorts of applications in many different fields of study. When a sequence of elementary row operations is performed on an augmented matrix, the linear system that corresponds to the resulting augmented matrix is equivalent to the original system. Our strategy in solving linear systems, therefore, is to take an augmented matrix for a system and carry it by means of elementary row operations to an equivalent augmented matrix from which the solutions of the system are easily obtained. www.math.hmc.edu /calculus/tutorials/linearsystems   (717 words)

 Systems of 3 Variable Linear Equations: How to solve these systems of planes...   (Site not responding. Last check: ) Systems of equations that have three variables are systems of planes. Like systems of linear equations, the solution of a system of planes can be no solution, one solution or infinite solutions. Before attempting to solve systems of three variable equations using elimination, you should probably be comfortable solving 2 variable systems of linear equations using elimination www.mathwarehouse.com /algebra/planes/systems/three-variable-equations.php   (453 words)

 BioMath: Linear Functions Here, we discuss solving linear equations beginning with a linear equation in one variable, and then solving a system of two linear equations by two different methods. Solving a system of two linear equations is the equivalent of finding the point (x, y) where the two lines intersect. Substitution is a convenient method to solve systems of equations when one of the two equations has a coefficient of 1 on either x or y. www.biology.arizona.edu /BioMath/tutorials/Linear/LinearEquations.html   (1220 words)

 5.2 - Systems of Linear Equations in Two Variables Multiply one or both equations by a constant so that the least common multiple of the coefficients on the variable to be eliminated is obtained. After you solve the system of linear equations, substitute the values for a and b into the equation y = ax + b to get the model. The system of linear equations to solve is 4b + 21a = 5 and 21b + 129a = 14. www.richland.edu /james/lecture/m116/systems/elimination.html   (1297 words)

 math lessons - System of linear equations In mathematics and linear algebra, a system of linear equations is a set of linear equations such as Systems of linear equations belong to the oldest problems in mathematics and they have many applications, such as in digital signal processing, estimation, forecasting and generally in linear programming and in the approximation of non-linear problems in numerical analysis. An efficient way to solve systems of linear equations is given by the Gauss-Jordan elimination or by the Cholesky decomposition. www.mathdaily.com /lessons/System_of_linear_equations   (453 words)

 Solving Systems of Equations with Matrices I   (Site not responding. Last check: ) When we solve an equation that has only one variable, we are finding the value for that variable that makes the equation true. A system of equations is when we have more than one equation and more than one variable. We refer to this as a system of equations, meaning that we want x and y values that make BOTH equations true. www.algebralab.org /lessons/lesson.aspx?file=Algebra_matrix_systems.xml   (287 words)

 Systems of Linear Equations   (Site not responding. Last check: ) Find N. Try to find the system of equations that needs to be solved and then look at the Solution using Maple. The previous two examples show instances of systems of linear equations with a unique solution. A system of linear equations could have no solution (e.g. omega.albany.edu:8008 /mat220dir/systems.html   (320 words)

 Solution of a System of Linear Equations, how to solve systems using substitution, the equations of the lines ... Systems have no solution when the lines are parallel (ie have the same slope) and the lines have different y-intercepts. The solution of the system of equations on the left is (2,2) which marks the point where the two lines intersect. This system of lines is the same system that we looked at in the last example. www.mathwarehouse.com /algebra/linear_equation/systems-of-equation   (1086 words)

 Equations These may not be exactly the words you used when you were solving a system of linear equations, but you did all these things. We performed the same steps both times because the steps involved in solving a system of equations depend only on the matrix that is to the left of the bar. If we want to solve a system of equations with the same matrix A for different b vectors that we will be given at a later time, it would be nice if we did not have to do Gauss-Jordan elimination every time. ceee.rice.edu /Books/LA/equations/index.html   (1977 words)

 Kristi M Students will be able to solve a system of linear equations by graphing. Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency – mentally or with paper and pencil in simple cases and using technology in all cases. Definition:  A system of linear equations is two or more linear equations using the same      variables. bama.ua.edu /~hardi001/lineareqlesson.htm   (835 words)

 Mathlets: Systems of Linear Equations   (Site not responding. Last check: ) Graphs the two lines associated with a system of two linear equations in two variables, showing the solution of the system as the point where the lines intersect (if a unique solution exists). The labels under the text input field tell whether the system is independent, dependent, or inconsistent, and in the independent case also give the coordinates of the solution point (where the two lines cross). In this case, the two equations describe the same line, and all points on that line are solutions of the system. cs.jsu.edu /mcis/faculty/leathrum/Mathlets/linear.html   (238 words)

 Math 310 - Glossary of Linear Algebra Terms A least-squares solution to a system of linear equations Ax = b is a vector x that minimizes the length of the vector Ax - b. The nullity of a linear transformation is the dimension of its null space. The rank of a linear transformation (and hence of any matrix regarded as a linear transformation) is the dimension of its range. www.math.uic.edu /~math310/glossary.html   (1060 words)

 Linear Algebra - System of Equations Multiply one of the equation with an appropriate real number that will eliminate one of the variables when the equations are added together. Multiply the first equation with 1 and add the first equation to the second. Solving system of three equations in three variables is similar to solving system with two variables. library.thinkquest.org /10030/10lsoeq.htm   (156 words)

 Solutions of Systems of Linear Equations The essential idea here is that we solve one of the equations for one of the unknowns, and then substitute the result into the other equation. Not all the systems are so nice and neat; after going through this process you might end up with fewer equations than variables, or equations that contradict each other. In the first case you have a system with infinitely many solutions ; in the second, the system is inconsistent and so has no solutions at all. www.math.csusb.edu /math110/src/systems/solving.html   (440 words)

 C++ Builder Tutorials - System of Linear Equations There are usually three types of approach to solving this system: by graph, by substitution, or elimination by addition. That is, you select either a, b, c, or d and solve the equation by that factor. As convenient as this design is, it doesn't solve much problem, the user may still be confused with typing an equation such as -5x-2y=-10. www.functionx.com /bcb/applications/linearequations.htm   (531 words)

 Solving Systems of Linear Equations Using Matrices The matrix method of solving systems of linear equations is just the elimination method in disguise. Make sure all equations are in standard form (Ax + By = C), and use the coefficients of each equation to form each row of the matrix. The same method can be used for n linear equations in n unknowns; in this case you would create an n × (n + 1) matrix, and use the matrix row operations to get the identity n × n matrix on the left side. hotmath.com /hotmath_help/algebra1/solving_systems_of_linear_equations_using_matrices.html   (289 words)

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