What is an augmented matrix?
Consists of the coefficient matrix with an added column containing the constants from the right sides of the equations.
An augmented matrix is a representation of a linear system of equations in matrix form that includes a column of constants on the right side of the vertical line separating the coefficient matrix from the constants. Specifically, an augmented matrix for a system of n linear equations with m variables is an (n x m+1) matrix of the form:
[ a11 a12 … a1m | b1 ]
[ a21 a22 … a2m | b2 ]
[ . . . . | . ]
[ an1 an2 … anm | bn ]
where aij represents the coefficients of the variables in the equations and bi the constants on the right-hand side, separated by a vertical bar. The augmented matrix is a convenient tool for solving a system of linear equations using row reduction operations, which transform the system of equations into an equivalent system that is easier to solve. Row reduction involves manipulating the rows of the augmented matrix to obtain a row-echelon form or a reduced row-echelon form that reveals the solution to the system of equations, if one exists.
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