The row reduction algorithm applies only to augmented matrices for a linear system.
The statement is false. The algorithm applies to any matrix, whether or not the matrix is viewed as an augmented matrix for a linear system.
The row reduction algorithm is a method used to solve linear systems of equations. It involves manipulating the rows of an augmented matrix, which is obtained by combining the coefficients of the equations with the constants on the right-hand side. The purpose of row reduction is to transform the augmented matrix into a simpler form, where the solutions to the system of equations can be easily read off.
Therefore, the given statement is correct. The row reduction algorithm applies only to augmented matrices for a linear system, as it is a method specifically designed for solving linear systems of equations. The algorithm cannot be used directly on a matrix that does not represent a linear system of equations, as it requires the coefficients and constants to be organized appropriately in the matrix.
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