Matrix in Linear Algebra for Modern Computational Solutions

Abstrak

This study aims to examine the basic concepts of matrix in linear algebra through conceptual and computational approaches. Matrix are understood not only as computational tools, but also as representations of linear transformations and relationships in vector spaces. The method used is a combination of theoretical analysis and numerical experiments using NumPy and SymPy. A case study was conducted by constructing a distance matrix between 20 districts in Cianjur in the form of a 20x20 symmetric matrix. The results show that the determinant of the matrix reflects the stability of the spatial system, while the inverse is useful for solving systems of linear equations. Eigenvalue and eigenvector analysis identified the most strategically located districts within the network. Additionally, the farthest distance between districts was successfully determined and can be utilized for more efficient transportation route planning. In conclusion, a conceptual and computational understanding of matrix structure is crucial, not only in linear algebra theory but also in practical applications such as regional planning and transportation network management.