Paul's Online Math Notes at Lamar University offers definitions and instructions on solving augmented matrices. It goes through several operations that can be used to manipulate augmented matrices to help solve a system of equations.
Know MorePaul's Online Math Notes describes how to convert a system of equations into an augmented matrix, moving the coefficients of each variable in each equation into the left side of the matrix, and moving the constants on the right side. It then defines some matrix operations that can manipulate the augmented matrix, such as interchanging rows, multiplying a row by a constant and adding one row to another row. It then uses these operations to go through a process called Gauss-Jordan elimination to solve an augmented matrix. The intent of Gauss-Jordan elimination is to produce the identity matrix on the left side of the augmented matrix and the solutions to the equation on the right side.
Purplemath also offers a page explaining the basics of augmented matrices and converting a linear system to an augmented matrix. Tutorvista provides several examples on how to solve simple augmented matrices when dealing with just two variables.
Learn more about AlgebraIn everyday applications, matrices are used to represent real-world data, such as the traits and habits of a certain population. They are used in geology to measure seismic waves. Matrices are rectangular arrangements of expressions, numbers and symbols that are arranged in columns and rows. Matrices have "m" number of rows and "n" number of columns, and numbers in a matrix are called entities or entries.
Full Answer >There are several applications of matrices in multiple branches of science and different mathematical disciplines. Most of them utilize the compact representation of a set of numbers within a matrix.
Full Answer >To solve two-step equations, simplify both sides of the equation by removing extra terms, then remove coefficients. It's also possible that a variable will exist on both sides of the equation. In this case, you need to isolate the variable.
Full Answer >To solve one-step equations, perform the correct mathematical operation to get the variable by itself, and perform the same operation on the other side of the equation. Solve the equation when the variable is by itself.
Full Answer >