The row reduction algorithm applies only to augmented matric

The row reduction algorithm applies only to augmented matrices for a linear system.

Is this statement true or false?

A.

The statement is false. It is possible to create a linear system such that the row reduction algorithm does not apply to the corresponding augmented matrix.

B.

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.

C.

The statement is true. Every matrix with at least two columns can be interpreted as the augmented matrix of a linear system.

D.

The statement is true. The row reduction algorithm is only useful when it is used to find the solution of a linear system.

Solution

We proceed by Elimination Method.

Since the statement is not true, we can easily eliminate options C and D.

Now, since for every linear system we can form an augmented matrix, and any matrix can be reduced by Row Reduction Algorithm because the matrix is not aware where it came from, thus the reasoning in option A stands false.

Thus, we are left with the correct answer B.

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.