Why did James Sylvester use the Matrix Theory?

James Sylvester utilized Matrix Theory to advance the study of linear algebra and its applications in various mathematical fields. He aimed to explore the properties of matrices and their determinants, contributing to the understanding of linear transformations and systems of equations. By formalizing these concepts, Sylvester laid the groundwork for future developments in both pure and applied mathematics, influencing areas such as statistics and physics. His work helped establish matrices as a fundamental tool in modern mathematics.