All of the concepts and terminology central to linear algebra were established in the late 19th century.
Following recent comments by user KCd, that in the early 20th century determinants were the “primary language of linear algebra”, I conclude (rightly or wrongly) that linear algebra originally focused on techniques for solving systems of linear equations and the role of matrices and their determinants.
Today, the focus of linear algebra is the study of vector spaces and their properties.
Who were the mathematicians that brought about this change of emphasis? Was there a particular paper or textbook, or was this change simply the result of a natural move towards a more abstract presentation of the subject?