Final answer:
The statement is true because the magnitude of a vector, which is determined by the Pythagorean theorem, is always a non-negative value, regardless of the sign of its scalar components.
Step-by-step explanation:
The statement that the scalar components of a two-dimensional vector may both be negative, but the scalar magnitude of the vector is always positive is true. This is because the scalar magnitude of a vector is a measure of its size or length without regard to its direction. Even if a two-dimensional vector has negative components, indicating that it points in the negative x and/or y direction on a coordinate system, the magnitude is calculated using the Pythagorean theorem and is always a non-negative value.
For example, if the negative scalar is -2 and the vector Ā has a length of 1.5, then the new vector Ā = -2Ā has a length C = |-2|A = 3.0 units, which is positive and indicates an increase in size while being antiparallel to the original vector.