Question

If two matrices are equivalent, then can one be transformed into the other with a sequence of elementary row operations?

1) True
2) False

Answer 1

Two equivalent matrices can be transformed into each other using elementary row operations such as row swapping, scalar multiplication, and row addition.

Step-by-step explanation:

The statement is true. If two matrices are equivalent, one can indeed be transformed into the other using a sequence of elementary row operations. Elementary row operations include swapping two rows, multiplying a row by a non-zero scalar, and adding a multiple of one row to another row. These operations are used in various matrix algorithms, such as Gaussian elimination, to simplify matrices and solve systems of linear equations.