**Definition:** If \(T: V 	o W\) is a linear transformation and \(c\) is a scalar, the *scalar multiple* \(cT\) is defined pointwise:
\[(cT)(\mathbf{v}) = c \cdot T(\mathbf{v}) \quad 	ext{for all } \mathbf{v} \in V\]

The transformation \(cT\) scales every output of \(T\) by the factor \(c\).

**Example:** If \(T(x,y) = (2x, 3y)\) and \(c = 5\), then \((5T)(x,y) = (10x, 15y)\).

**Example:** If \(D\) is the derivative operator on polynomials, then \((3D)(p) = 3p'\).