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Linear algebra is a branch of mathematics that deals with the study of linear equations and their representations in vector spaces. It involves the manipulation of matrices, vectors, and other mathematical objects to solve problems related to systems of linear equations, transformations, and more.
Linear algebra has a wide range of applications in fields such as physics, engineering, computer science, economics, and statistics. It is used to solve problems related to data analysis, computer graphics, optimization, signal processing, and many other areas.
Matrices are rectangular arrays of numbers or other mathematical objects. They are manipulated using various operations such as addition, subtraction, multiplication, and division. These operations follow specific rules and can be used to solve systems of linear equations, find inverse matrices, and perform other calculations.
Algebraic manipulation involves solving equations using algebraic operations such as addition, subtraction, multiplication, and division. Matrix manipulation, on the other hand, involves working with matrices and performing operations such as matrix multiplication, finding determinants, and calculating eigenvalues and eigenvectors.
Linear algebra is a fundamental tool in machine learning and artificial intelligence. It is used to represent and manipulate data in the form of vectors and matrices, perform calculations and transformations, and build algorithms for tasks such as pattern recognition, classification, and prediction.