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- https://math.libretexts.org/Courses/Chabot_College/Chabot_College_College_Algebra_for_BSTEM/07%3A_Systems_of_Equations_and_Inequalities/7.06%3A_Solving_Systems_with_Gaussian_EliminationA matrix can serve as a device for representing and solving a system of equations. To express a system in matrix form, we extract the coefficients of the variables and the constants, and these become ...A matrix can serve as a device for representing and solving a system of equations. To express a system in matrix form, we extract the coefficients of the variables and the constants, and these become the entries of the matrix. We use a vertical line to separate the coefficient entries from the constants, essentially replacing the equal signs. When a system is written in this form, we call it an augmented matrix.
- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/A_First_Journey_Through_Linear_Algebra/01%3A_Systems_of_Equations/1.03%3A_Gaussian_EliminationThe work we did in the previous section will always find the solution to the system. In this section, we will explore a less cumbersome way to find the solutions. First, we will represent a linear sys...The work we did in the previous section will always find the solution to the system. In this section, we will explore a less cumbersome way to find the solutions. First, we will represent a linear system with an augmented matrix. A matrix is simply a rectangular array of numbers. The size or dimension of a matrix is defined as m×n where m is the number of rows and n is the number of columns.
- https://math.libretexts.org/Courses/Northeast_Wisconsin_Technical_College/College_Algebra_(NWTC)/07%3A_Systems/7.07%3A_Solving_Systems_with_Gaussian_EliminationA matrix can serve as a device for representing and solving a system of equations. To express a system in matrix form, we extract the coefficients of the variables and the constants, and these become ...A matrix can serve as a device for representing and solving a system of equations. To express a system in matrix form, we extract the coefficients of the variables and the constants, and these become the entries of the matrix. We use a vertical line to separate the coefficient entries from the constants, essentially replacing the equal signs. When a system is written in this form, we call it an augmented matrix.
- https://math.libretexts.org/Under_Construction/Purgatory/MAT_1320_Finite_Mathematics/03%3A_Solving_Systems_of_Equations/3.03%3A_Solving_Systems_with_Gaussian_EliminationA matrix can serve as a device for representing and solving a system of equations. To express a system in matrix form, we extract the coefficients of the variables and the constants, and these become ...A matrix can serve as a device for representing and solving a system of equations. To express a system in matrix form, we extract the coefficients of the variables and the constants, and these become the entries of the matrix. We use a vertical line to separate the coefficient entries from the constants, essentially replacing the equal signs. When a system is written in this form, we call it an augmented matrix.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Map%3A_Linear_Algebra_(Waldron_Cherney_and_Denton)/03%3A_The_Simplex_Method/3.03%3A_Dantzig's_AlgorithmIn simple situations a graphical method might suffice, but in many applications there may be thousands or even millions of variables and constraints. Clearly an algorithm that can be implemented on a ...In simple situations a graphical method might suffice, but in many applications there may be thousands or even millions of variables and constraints. Clearly an algorithm that can be implemented on a computer is needed. The simplex algorithm (usually attributed to George Dantzig) provides exactly that.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/A_First_Course_in_Linear_Algebra_(Kuttler)/01%3A_Systems_of_Equations/1.03%3A_Gaussian_EliminationThe work we did in the previous section will always find the solution to the system. In this section, we will explore a less cumbersome way to find the solutions. First, we will represent a linear sys...The work we did in the previous section will always find the solution to the system. In this section, we will explore a less cumbersome way to find the solutions. First, we will represent a linear system with an augmented matrix. A matrix is simply a rectangular array of numbers. The size or dimension of a matrix is defined as m×n where m is the number of rows and n is the number of columns.
- https://math.libretexts.org/Courses/Mission_College/Math_001%3A_College_Algebra_(Kravets)/07%3A_Systems_of_Equations_and_Inequalities/7.06%3A_Solving_Systems_with_Gaussian_EliminationA matrix can serve as a device for representing and solving a system of equations. To express a system in matrix form, we extract the coefficients of the variables and the constants, and these become ...A matrix can serve as a device for representing and solving a system of equations. To express a system in matrix form, we extract the coefficients of the variables and the constants, and these become the entries of the matrix. We use a vertical line to separate the coefficient entries from the constants, essentially replacing the equal signs. When a system is written in this form, we call it an augmented matrix.
- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/MAT_149%3A_Topics_in_Finite_Mathematics_(Holz)/03%3A_Systems_and_Matrices/3.02%3A_Matrices/3.2.01%3A_Gaussian_EliminationThe work we did in the previous section will always find the solution to the system. In this section, we will explore a less cumbersome way to find the solutions. First, we will represent a linear sys...The work we did in the previous section will always find the solution to the system. In this section, we will explore a less cumbersome way to find the solutions. First, we will represent a linear system with an augmented matrix. A matrix is simply a rectangular array of numbers. The size or dimension of a matrix is defined as m×n where m is the number of rows and n is the number of columns.
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Stitz-Zeager)/08%3A_Systems_of_Equations_and_Matrices/8.02%3A_Systems_of_Linear_Equations-_Augmented_MatricesWe previously introduced Gaussian Elimination as a means of transforming a system of linear equations into triangular form with the ultimate goal of producing an equivalent system of linear equations ...We previously introduced Gaussian Elimination as a means of transforming a system of linear equations into triangular form with the ultimate goal of producing an equivalent system of linear equations which is easier to solve. If we study the process, we see that all of our moves are determined entirely by the coefficients of the variables involved, and not the variables themselves. In this section, we introduce a bookkeeping device to help us solve systems of linear equations.
- https://math.libretexts.org/Bookshelves/Algebra/Algebra_and_Trigonometry_1e_(OpenStax)/11%3A_Systems_of_Equations_and_Inequalities/11.06%3A_Solving_Systems_with_Gaussian_EliminationA matrix can serve as a device for representing and solving a system of equations. To express a system in matrix form, we extract the coefficients of the variables and the constants, and these become ...A matrix can serve as a device for representing and solving a system of equations. To express a system in matrix form, we extract the coefficients of the variables and the constants, and these become the entries of the matrix. We use a vertical line to separate the coefficient entries from the constants, essentially replacing the equal signs. When a system is written in this form, we call it an augmented matrix.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/01%3A_Systems_of_Equations/1.04%3A_Balancing_Chemical_ReactionsThe tools of linear algebra can also be used in the subject area of Chemistry, specifically for balancing chemical reactions.
