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He also realized the connection between matrices and determinants, and wrote “There would be many things to say about this theory of matrices which should, it seems to me, precede the theory of determinants”. 1900, a theory of linear transformations of finite-dimensional vector spaces had emerged. Gaussian elimination and matrix decompositions, and linear algebra became an essential tool for modelling and simulations. Linear algebra first appeared in American graduate textbooks in the 1940s and in undergraduate textbooks in the 1950s.