2012 is Alan Turing Year but perhaps I have missed a chance to attract attention of my colleagues who, like me, teach undergraduate linear algebra to a significant fact in history of linear algebra which is worth mentioning to students:
“the advent of electronic computers“.
I told the story to my students in my lecture on Wednesday. Since the idea that
“The process of replacing the rows of a matrix by a linear combination of other rows may be regarded as left-multiplication of the matrix by another matrix, this second matrix having coefficients which describe the linear combinations required” [1948, p. 290]
comes forth at early stages of modern expositions of linear algebra, this semester’s courses are likely to pass the point when history of LU decomposition could be usefully mentioned. But maybe it is not too late to do that in linear algebra courses taught in the Autumn.
 A. M. Turing, Rounding-off errors in matrix processes. Quart. J Mech. Appl. Math. 1 (1948), 287–308.