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Consider the linear system of equations AX = Y
where
X is a n x 1 matrix of variables,
Y is a n x 1 matrix of constants, and
A is an n x n matrix of coefficients.
Provided A is not a singular matrix, A has an inverse, A-1, an n x n matrix.
Premultiplying by A-1 gives A-1AX = A-1Y or X = A-1Y, the solution to the linear system.
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What is the relationship between linear algebra and economics?
Many problems in economics can be modelled by a system of linear equations: equalities r inequalities. Such systems are best solved using matrix algebra.
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There are more than two methods, and of these, matrix inversion is probably the easiest for solving systems of linear equations in several unknowns.
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A matrix is a field of numbers with rows and columns. Matrices can represent many different things and have numerous applications. For example, they can be used for solving systems of linear equations or working with linear transformations; in multiple regression analyses, for working with vectors.
What does the backslash operator do in MATLAB and how is it used in matrix operations?
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What is the relationship between linear algebra and economics?
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What has the author Kent Franklin Carlson written?
Kent Franklin Carlson has written: 'Applications of matrix theory to systems of linear differential equations' -- subject(s): Differential equations, Linear, Linear Differential equations, Matrices
What are 2 symbolic techniques used to solve linear equations and which is better?
There are more than two methods, and of these, matrix inversion is probably the easiest for solving systems of linear equations in several unknowns.
What has the author Dennis S Bernstein written?
Dennis S. Bernstein has written: 'Matrix mathematics' -- subject(s): Matrices, Linear systems
Where is Matrix Systems Inc. located?
Matrix Systems Inc. is located in Miamisburg, Ohio, USA.
How does the biconjugate gradient method improve upon the traditional conjugate gradient method for solving linear systems of equations?
The biconjugate gradient method is an extension of the conjugate gradient method that can solve a wider range of linear systems of equations by working with non-symmetric matrices. It uses two different conjugate directions to speed up convergence and improve accuracy compared to the traditional conjugate gradient method.
