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**Unformatted text preview: **Lecture 20. Gaussian Elimination Nguyen Thi Thu Hang K 53 Advanced Math Class Hanoi University of Science 20 th October, 2011 Nguyen Thi Thu Hang Lecture 20. Gaussian Elimination Lecture 20. Gaussian Elimination Nguyen Thi Thu Hang Lecture 20. Gaussian Elimination Lecture 20. Gaussian Elimination Nguyen Thi Thu Hang Lecture 20. Gaussian Elimination Lecture 20. Gaussian Elimination Solving systems of linear equations. Nguyen Thi Thu Hang Lecture 20. Gaussian Elimination Lecture 20. Gaussian Elimination Solving systems of linear equations. Find the rank of a matrix Nguyen Thi Thu Hang Lecture 20. Gaussian Elimination Lecture 20. Gaussian Elimination Solving systems of linear equations. Find the rank of a matrix Calculate the determinant of a matrix Nguyen Thi Thu Hang Lecture 20. Gaussian Elimination Lecture 20. Gaussian Elimination Solving systems of linear equations. Find the rank of a matrix Calculate the determinant of a matrix Calculate the inverse of an invertible square matrix. Nguyen Thi Thu Hang Lecture 20. Gaussian Elimination Lecture 20. Gaussian Elimination Solving systems of linear equations. Find the rank of a matrix Calculate the determinant of a matrix Calculate the inverse of an invertible square matrix. The algorithm is named after Gauss but it was not invented by him. Nguyen Thi Thu Hang Lecture 20. Gaussian Elimination Gaussian elimination Nguyen Thi Thu Hang Lecture 20. Gaussian Elimination Gaussian elimination How do you solve an equations system? Ax = b Where A is an n × n matrix and b is a vector in R n . Nguyen Thi Thu Hang Lecture 20. Gaussian Elimination Gaussian elimination How do you solve an equations system? Ax = b Where A is an n × n matrix and b is a vector in R n . Gaussian elimination Is the simplest way and also the standard method of solving equations system. Nguyen Thi Thu Hang Lecture 20. Gaussian Elimination Gaussian elimination How do you solve an equations system? Ax = b Where A is an n × n matrix and b is a vector in R n . Gaussian elimination Is the simplest way and also the standard method of solving equations system. Definition An unit low triangular matrix is a matrix with all of it diagonal entries are equal to 1. Nguyen Thi Thu Hang Lecture 20. Gaussian Elimination Idea of Gaussian elimination Nguyen Thi Thu Hang Lecture 20. Gaussian Elimination Idea of Gaussian elimination To apply Gaussian elimination, matrix A should has LU factorization. Nguyen Thi Thu Hang Lecture 20. Gaussian Elimination Idea of Gaussian elimination To apply Gaussian elimination, matrix A should has LU factorization. Nguyen Thi Thu Hang Lecture 20. Gaussian Elimination Idea of Gaussian elimination To apply Gaussian elimination, matrix A should has LU factorization....

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