ABSTRACT
Linear algebra is the branch of mathematics that deals with vector spaces and linear transformations. For someone just beginning their study of linear algebra, that is probably a meaningless statement. Matrices are the most common way of representing vectors and linear transformations and play a central role in nearly every computation in linear algebra. The size of a matrix is described by its dimensions; i.e., the number of rows and columns in the matrix, with the number of rows given first. Multiplying any two “compatible” matrices. In order to be compatible for multiplication, the matrix on the left must have the same number of entries in a row as there are entries in a column of the matrix on the right. Historically, determinants were used before matrices. Originally, a determinant was defined as a property of a system of linear equations. There, the determinant “determines” whether the system has a unique solution.
