In this section we specialize further and consider matrices with equal numbers of rows and columns, which when considered as coefficient matrices lead to systems with equal numbers of equations and variables. We will see in the second half of the course (Chapter D, Chapter E, Chapter LT, Chapter R) that these matrices are especially important.

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##### Definition of nonsingular matrix: the associated homogeneous linear system has only the trivial solution math.la.d.mat.nonsingular.z

##### Definition of singular matrix math.la.d.mat.singular