Matrix Algebra: Gaussian Elimination Method

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra. In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra. Here is the sixth topic where we talk about solving a set of simultaneous linear equations using Gaussian elimination method – both Naive and partial pivoting methods are discussed. How to find determinants by using the forward elimination step of Gaussian elimination is also discussed.  Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation. Gaussian Elimination Method
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Matrix Algebra: System of Equations

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra. In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra. Here is the fifth topic where we talk about setting up simultaneous linear equations in matrix form, consistent and inconsistent system of equations, the rank of a matrix, conditions when unique, infinite number or no solutions exist, and finding the inverse of a square matrix.  Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation. System of Equations
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Matrix Algebra: Unary Operations

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra. In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra. Here is the fourth topic where we talk about unary operations on a matrix including transpose, symmetry, determinant, and trace of a matrix.  Methods of finding determinants along with some fundamental theorems of determinants are discussed.  Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation. Unary Operations
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Matrix Algebra: Vectors

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra.

In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra.

Here is the second topic where we talk about vectors, binary operations on vectors, set up the concept of linear combination and linear independence of vector.  Learn how vectors are used to set up simultaneous linear equations.  Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation.

Vectors


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Matrix Algebra: Binary Operations

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra.

In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra.

Here is the third topic where we talk about binary operations of matrices – subtraction, addition, and multiplication.  Linear combination of matrices and rules of binary operations are discussed. Get all the resources in form of textbook content, lecture videos, multiple choice test, problem set, and PowerPoint presentation.

Binary Operations


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Matrix Algebra: Introduction

Many university STEM major programs have reduced the credit hours for a course in Matrix Algebra or have simply dropped the course from their curriculum.   The content of Matrix Algebra in many cases is taught just in time where needed.  This approach can leave a student with many conceptual holes in the required knowledge of matrix algebra.

In this series of blogs, we bring to you ten topics that are of immediate and intermediate interest for Matrix Algebra.

Here is the first topic where we define a matrix, vector, submatrix, square matrix, triangular matrix (upper and lower), diagonal matrix, identity matrix, and diagonally dominant matrix.  Get the information in form of textbook content, lecture videos, multiple choice test, problem set and PowerPoint presentation.

Introduction 


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How much computational time does it take to find the inverse of a square matrix using Gauss Jordan method?  Part 1 of 2.

Problem Statement

How much computational time does it take to find the inverse of a square matrix using Gauss Jordan method?  Part 1 of 2.

Solution

To understand the solution, you should be familiar with the Gauss Jordan method of finding the inverse of a square matrix.  Peter Young of UCSC describes it briefly in this pdf file while if you like watching an example via a video, you can see PatrickJMT doing so.  You also need to read a previous blog where we calculated the computational time needed for the forward elimination steps on a square matrix in the Naïve Gauss elimination method.   We are now ready to estimate the computational time required for Gauss Jordan method of finding the inverse of a square matrix.

GJ Inverse Blog

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