The equation T(cu) = cT(u) represents a property of linear transformations in mathematics. Here, T is a linear transformation, c is a scalar (a constant number), and u is a vector. This equation states that when a vector u is scaled by c , the transformation T applied to this scaled vector is the same as scaling the transformed vector T(u) by the same factor c . This property is essential in various fields, including physics, engineering, and computer science, as it ensures that linear transformations maintain proportional relationships. It highlights the consistency of linear systems, making them easier to analyze and understand. Linear transformations are foundational in areas such as vector spaces and matrix theory.