3.6 RANK OF A MATRIX
The ideas such as subspace and linear independence, developed in the context of vector spaces, also help us in gaining useful insights about individual matrices. In this section, we use the ideas to examine the important concept of the rank of a matrix.
Consider any A ∈ Mm×n(
). Each of the m rows of A, considered an n-dimensional row vector, is a vector in the vector space 
. Similarly, the m-dimensional column vectors of A can be considered as vectors in .
Definition 3.6.1. Given A ∈ Mm×n(), the subspace of spanned by the ...
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