Algebra Series - Concepts and Formulas™
Types of Matrices, Matrix Solutions of Systems of Linear Equations (ALG-CF17)

This sheet provides a comprehensive review of all of the most important topics, concepts and formulas thoroughly covering types of matrices, matrix solutions of systems of linear equations, explained in detail, with detailed illustrations. Unlike charts and notes, this Concepts and Formulas™ sheet anticipates and answers questions about how to use the concepts - how to solve problems with them, it doesn't just list facts and formulas.

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Topics Covered:

• Diagonal matrices
• Multiplicative Identity matrices of order n
• Fundamental properties of square matrices
• Matrix solutions of systems of linear equations
• Coefficient matrices
• Augmented matrices
• Row-Equivalent matrices
• Elementary Row Operations
• Elementary System Operations and their corresponding Elementary Row Operations
• How to solve a three-variable linear system in matrix form by Gaussian Elimination
• Matrices in Echelon form
• Matrices in Reduced Echelon form
• Gauss-Jordan Elimination
• Multiplicative Inverse of a matrix
• Singular and Nonsingular matrices
• Grafted matrices

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