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This algebra 2 math tutorial from NutshellMath offers help with augmented matrices and using them to solve systems of equations. An augmented matrix is a matrix containing the coefficients and constants from a system of equations. Each row of the matrix represents one of the equations in the system, and a vertical bar separates the coefficients of the variables and the constants on the other side of the equal sign. Using an augmented matrix permits the use of Gaussian Elimination, simple matrix row operations used to solve the system of equations easily.
When solving a system of equations using an augmented matrix, it is necessary to first set up the matrix with the coefficients of the variables in the proper place and the constants on the right side of a vertical bar. The goal of solving a system of equations using an augmented matrix is to use row operations to turn the left side of the augmented matrix into the identity matrix. To do so, it may be necessary to switch one row with another or add one row to another. It is also permitted to multiply any row by a constant or multiply a row and add it to another. Using a combination of these operations, it is possible to solve for the identity matrix and find the solution to the system of equations. The solution can be expressed as an ordered pair of the constants of the right side of the matrix.
Some special cases exist when solving using augmented matrices, in cases where it is not possible to obtain the identity matrix. These cases are presented in the tutorial, and will yield no solution or infinite solutions to the system of equations.
Augmented matrices are powerful tools used to quickly and easily solve systems of equations. Mastering this application of matrices is an important asset in algebra.
This algebra 2 math tutorial from NutshellMath offers help with augmented matrices and using them to solve systems of equations. An augmented matrix is a matrix containing the coefficients and constants from a system of equations. Each row of the matrix represents one of the equations in the system, and a vertical bar separates the coefficients of the variables and the constants on the other side of the equal sign. Using an augmented matrix permits the use of Gaussian Elimination, simple matrix row operations used to solve the system of equations easily.
When solving a system of equations using an augmented matrix, it is necessary to first set up the matrix with the coefficients of the variables in the proper place and the constants on the right side of a vertical bar. The goal of solving a system of equations using an augmented matrix is to use row operations to turn the left side of the augmented matrix into the identity matrix. To do so, it may be necessary to switch one row with another or add one row to another. It is also permitted to multiply any row by a constant or multiply a row and add it to another. Using a combination of these operations, it is possible to solve for the identity matrix and find the solution to the system of equations. The solution can be expressed as an ordered pair of the constants of the right side of the matrix.
Some special cases exist when solving using augmented matrices, in cases where it is not possible to obtain the identity matrix. These cases are presented in the tutorial, and will yield no solution or infinite solutions to the system of equations.
Augmented matrices are powerful tools used to quickly and easily solve systems of equations. Mastering this application of matrices is an important asset in algebra.