This lecture explains how to determine the Jacobian matrix of a differentiable function, emphasizing the importance of correctly identifying the function and point of calculation. Through a step-by-step analysis of multiple choice answers, the instructor clarifies the process of deriving the Jacobian matrix and highlights the significance of matrix dimensions in the context of the given function. By comparing the characteristics of each option, the correct answer is revealed to be option B, showcasing the application of theoretical knowledge in practical scenarios.