Matrix Algebra Explained

What you’ll learn
How to Solve Linear Systems Using Gaussian Elimination
How to Solve Linear Systems Using Gauss-Jordan Elimination
How to Place an Augmented Matrix in Row Echelon Form
How to Place an Augmented Matrix in Reduced Row Echelon Form
How to Add Matrices
How to Subtract Matrices
How to Multiply a Matrix by a Scalar
How to Multiply Matrices
How to Find the Inverse of a Matrix using Row Reduction
How to Solve Linear Systems using Matrix Equations (Using the Inverse of a Matrix)
How to Find the Determinant of a Matrix Using Laplace Expansion
How to Find the Determinant of a 3 x 3 Matrix Using the Shortcut
How to Find the Determinant of a Matrix in Upper Triangular Form 4 x 4 Shortcut
How to Find the Transpose of a Matrix
How to Find the Classical Adjoint (Adjugate of a Matrix)
How to Find the Inverse of a Matrix Using the Determinant and the Adjoint (Adjugate)
How to Solve a 2 x 2 Linear System Using Cramer’s Rule
How to Solve a 3 x 3 Linear System Using Cramer’s Rule
Applications of Determinants – Finding the Area of a Triangle
Applications of Determinants – Testing for Collinearity
Applications of Determinants – Finding the Equation of a Line Using Determinants

Requirements
Algebra 1
Algebra 2 is helpful but not required

Description
In this course, you will master the basics of matrices in algebra. While this is not a linear algebra course, it will serve to get you up to speed with most of the entry level topics taught in a linear algebra course. In this course, you will learn the following:How to Solve Linear Systems Using Gaussian EliminationHow to Solve Linear Systems Using Gauss-Jordan EliminationHow to Place an Augmented Matrix in Row Echelon FormHow to Place an Augmented Matrix in Reduced Row Echelon FormHow to Add MatricesHow to Subtract MatricesHow to Multiply a Matrix by a ScalarHow to Multiply MatricesHow to Find the Inverse of a Matrix using Row ReductionHow to Solve Linear Systems using Matrix Equations (Using the Inverse of a Matrix)How to Find the Determinant of a Matrix Using Laplace ExpansionHow to Find the Determinant of a 3 x 3 Matrix Using the ShortcutHow to Find the Determinant of a Matrix in Upper Triangular Form 4 x 4 ShortcutHow to Find the Transpose of a MatrixHow to Find the Classical Adjoint (Adjugate of a Matrix)How to Find the Inverse of a Matrix Using the Determinant and the Adjoint (Adjugate)How to Solve a 2 x 2 Linear System Using Cramer’s RuleHow to Solve a 3 x 3 Linear System Using Cramer’s RuleApplications of Determinants – Finding the Area of a TriangleApplications of Determinants – Testing for CollinearityApplications of Determinants – Finding the Equation of a Line Using Determinants

Who this course is for
Students who want to learn the basics of Linear Algebra and be able to work with Matrices