Flight performance of a Mars entry, descent, and landing system depends on the complex interaction between the guidance, navigation, and control system, mission concept of operations, trajectory design, vehicle configuration, actuators, disturbance accelerations and torques, environment modeling and atmospheric uncertainty, and top-level mission constraints. Consequently, analyzing a closed-loop, six degree-of-freedom guidance, navigation, and control system for atmospheric entry and powered descent and landing has traditionally required Monte Carlo analysis which generally implies extensive computational resources. This paper employs a previously derived linear covariance analysis formulation to quickly and reliably evaluate the guidance and navigation performance for a notional Mars entry, descent, and landing system to demonstrate precision landing. The analysis includes navigation performance, trajectory dispersions, propellant usage, and sensitivity analysis. A preliminary comparison between the linear covariance analysis and Monte Carlo results is provided. Results indicate good agreement between the linear covariance and Monte Carlo techniques.