page13 said:Thanks Dick. I guess I'll get some big ugly fractions in my Row Echelon Form, correct? So far I've got numbers over 53 in the 1st row, over 65 in the 2nd row, and the 3rd row looks like it'll be a 4 digit denominator.
Linear Algebra is a branch of mathematics that deals with linear equations and their representations in vector spaces. It involves the study of linear transformations, systems of linear equations, and matrices.
Gaussian Elimination is a method used to solve systems of linear equations by transforming them into row-echelon form, making it easier to find the solution. It involves applying elementary row operations to a matrix until it is in its reduced form.
The main purpose of using Gaussian Elimination is to simplify systems of linear equations and make it easier to solve them. It can also be used to find the inverse of a matrix, which is useful in various applications such as solving systems of differential equations and finding the least squares solution to a system of linear equations.
A row-echelon form is a matrix that has been simplified using Gaussian Elimination, where all leading coefficients are 1 and all entries below leading coefficients are 0. A reduced row-echelon form is a further simplified form where all leading coefficients are 1 and all other entries in the same column are also 0.
Linear Algebra and Gaussian Elimination have various applications in fields such as engineering, physics, economics, and computer science. For example, they can be used to solve systems of equations in circuit analysis, model physical systems in physics, optimize financial portfolios in economics, and perform image processing in computer science.