A traffic matrix is a network-wide description of the total traffic volume carried within a domain, where each element describes the volume of traffic that originates at one node and is destined for another, and corresponds to an origin destination (OD) pair. The Davao City local government implemented a project for traffic system with road sensors and CCTV (closed-circuit television) cameras but years after, some traffic lights appear to be blinking. It then takes a long time before the traffic lights restored to its usual function. Thus, not all of the intersection of streets in Davao City has traffic control. This study aimed to utilize matrix concepts on traffic control through computations using systems of linear equation and Gauss Jordan elimination involving actual traffic vehicle density data recorded from selected 4-cornered and 3-cornered blocks of Davao City. A descriptive method, specifically a mix of field survey and computational approach was utilized. The traffic matrix created indicates that for traffic to keep flowing in the 4-cornered block, 1430, 151, and 261 cars per hour must be routed between intersections 1 and 2, intersections 3 and 2, and intersections 3 and 4, respectively in an hour. For the 3-cornered block, 200, 711 and 1094 cars per hour need to be routed between intersections 1 and 2, 3 and 2 and 1 and 3, respectively. Then, the matrix is used to know how to organize the vehicles and control their entering and leaving a street to avoid traffic jam.