Write the system of equations associated with each augmented matrix . Do not solve.

Key Concepts

Augmented Matrix

An augmented matrix is a matrix that represents a system of linear equations. It combines the coefficients of the variables and the constants from the equations into a single matrix, where each row corresponds to an equation. The left side of the matrix contains the coefficients, while the right side contains the constants, separated by a vertical line or an additional column.

System of Linear Equations

A system of linear equations is a collection of two or more linear equations involving the same set of variables. The solutions to the system are the values of the variables that satisfy all equations simultaneously. Systems can have one solution, no solution, or infinitely many solutions, depending on the relationships between the equations.

Writing Equations from Matrices

To write the system of equations from an augmented matrix, one must interpret each row of the matrix as a separate equation. The coefficients in each row correspond to the variables, while the last column represents the constants. This process involves translating the matrix format back into standard equation form, ensuring that the relationships between the variables are accurately represented.