elementary row operations viewed as multiplication by
elementary matrices
row equivalent matrices
Note that elementary matrices are always invertible and
why.
Note Thm 1.5.3 "Equivalent Statements" concerning a square
matrix A. Understand what it says and what it does not say. This
theorem will gradually get longer as we move through the text.
Does say, for instance, that an invertible matrix can
always be expressed as a product of elementary matrices.
Does not say, however, that n x n matrices are always
invertible.
Note the method described in Examples 4 and 5 for either
finding the inverse of a given square matrix or showing that there
is no inverse.