Answer:
True
Explanation:
Row operations in a matrix correspond to the application of elementary operations to the system of linear equations represented by the matrix. These operations do not affect the linear dependence relations among the columns of the matrix because they preserve the solutions of the system of equations.
A linear dependence relation among the columns of a matrix means that there exist scalars (not all zero) such that a linear combination of the columns equals the zero vector. This relation can be expressed as a homogeneous system of linear equations, which has the same solutions as the original system of equations represented by the matrix.
When performing row operations on a matrix, the solutions of the system of equations are preserved, which means that the solutions of the homogeneous system and the linear dependence relations among the columns of the matrix are also preserved. Therefore, row operations do not affect linear dependence relations among the columns of a matrix.