Gaussian Elimination is a method for solving systems of linear equations by transforming the system's augmented matrix into a row-echelon form, from which the solutions can be easily obtained using back substitution. This technique is fundamental in linear algebra and is widely used in various fields, including engineering and computer science, for its straightforward computational approach.

Gaussian Elimination

solving systems of linear equations

An augmented matrix is a compact representation of a system of linear equations, combining the coefficient matrix and the constants into a single matrix. It is used in methods like Gaussian elimination to find solutions to the system by performing row operations that simplify the matrix into a form where the solutions become evident.

augmented matrix

row-echelon form

Back substitution is a method used to solve a system of linear equations that has been transformed into an upper triangular matrix form. It involves solving for the variables starting from the last equation and substituting these values back into the preceding equations to find all unknowns.

back substitution

Linear algebra is a branch of mathematics that deals with vector spaces and linear mappings between these spaces, focusing on the study of lines, planes, and subspaces. It is fundamental in various scientific fields, providing tools for solving systems of linear equations, performing transformations, and analyzing vector spaces and matrices.

linear algebra

computational approach

Engineering is the application of scientific and mathematical principles to design, build, and analyze structures, machines, and systems, aiming to solve real-world problems efficiently and sustainably. It encompasses a wide range of specialized fields that address various aspects of technology and innovation, driving progress in industries and improving quality of life.

engineering

Computer science is the study of algorithmic processes, computational machines, and computation itself, which underpins the development of software and systems that drive modern technology. It encompasses a wide range of topics from theoretical foundations to practical applications, making it essential for innovation in various fields such as artificial intelligence, cybersecurity, and data science.

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