This thesis introduces a continuous-time distributed algorithm designed to address a range of matrix analysis and computation problems in networked systems. Focusing initially on the Local-Equation Local-Variable (LELV) problem, the algorithm enables nodes within the network to collaboratively tackle six specific challenges. These include computing least-squares solutions to linear equations, determining the minimum-norm least-squares solution, detecting solution existence, computing the Moore-Penrose inverse of a matrix and identifying full column or row rank matrices. The algorithm, functioning as an affine, networked dynamical system, demonstrates global exponential convergence, supported by an explicit lower bound on its convergence rate. Furthermore, it offers deterministic guarantees for some problems while ensuring convergence with probability one for others. Extending the scope to include the Local-Equation Global-Variable (LEGV) problem, this thesis provides preliminary analysis, including equilibrium point analysis and simulation of the algorithm to demonstrate convergence. While minimal in-depth exploration was conducted, these initial insights highlight the algorithm’s potential applicability in addressing LEGV challenges within distributed environments. Overall, this thesis contributes a novel continuous-time distributed algorithm with significant implications for matrix computation in networked systems. Through rigorous theoretical analysis and initial exploration, it lays the groundwork for further research and practical applications in distributed computing settings.