Replace R_2 by R_2 + (- 3)R_1. begin{matrix} 1&3&-5 3&6&3 -4&9&1 end{matrix} middle |...

Understand what is reduced row-echelon form, and what are the row-echelon form rules. Using reduced row-echelon form examples, learn to write reduced form matrix.

Learn how to convert a linear system into matrix form and how to write an augmented matrix. See augmented matrix examples in order to learn how to solve them.

Learn how to solve systems of equations with three variables. Discover how to determine if the number of solutions for a linear system is singular, infinite, or none.

Understand eigenvalues and eigenvectors of a matrix. Compute eigenvalues using the characteristic equation. Practice finding eigenvalues for 2x2 and 3x3 matrices.

What is an inverse matrix? Learn about matrices and matrix inversion, and how to do an inverse matrix. Also, see examples of how to complete an inverse matrix.

A linear system with three variables is a collection of three linear equations in three variables, with none of the variables having assigned exponents. Practice the elimination method to discover how making variables 'disappear' provides a simplified solution.

Cramer's rule can be used to solve systems of linear equations in three variables. Learn about the linear system in three variables, the detailed explanation of Cramer's rule, and finding determinants to solve such equations.

A higher-order partial derivative is a function with multiple variables. Study the definition and examples of higher-order partial derivatives and mixed partial derivatives.

Learn how to solve a cubic function by factoring, synthetically dividing, and graphing. Study the cubic formula, and also see the solved examples of cubic equations.

Learn about matrix row operations to change matrix using various examples. Understand what a row matrix is. Also, know about the rules for adding matrices.

In mathematics, eigenvalues and eigenvectors are special values found in a square matrix. Explore the definition, equation, and examples of eigenvalues and eigenvectors. Understand how to find them, and recognize representative eigenvectors.

The Newton-Raphson method is a method used to find solutions for nonlinear systems of equations. Learn what the Newton-Raphson method is, how it is set up, review the calculus and linear algebra involved, and see how the information is packaged. Finally, explore how to solve a problem using this method with a step-by-step example.

Learn to identify a square matrix, its properties, and features. Perform addition and multiplication of square matrices. Find the square of a square matrix.

What are rational zeros? Learn the use of rational zero theorem and synthetic division to find zeros of a polynomial function. Cross-verify using the graph.

Learn to define composite functions. Discover the domain and range of composition of two functions. Learn how to find the domain and range of composite functions.

Understand what Newton's Method is. Learn about Newton's Method Formula and how to do Newton's Method. Get practical insights through various examples.