Various advanced texts in linear algebra prove the following determinant criterion for
Chapter 4, Problem 14(choose chapter or problem)
Various advanced texts in linear algebra prove the following determinant criterion for rank: The rank of a matrix A is r if and only if A has some submatrix with a nonzero determinant, and all square submatrices of larger size have determinant zero. [Note: A submatrix of A is any matrix obtained by deleting rows or columns of A. The matrix A itself is also considered to be a submatrix of A.] In each part, use this criterion to find the rank of the matrix.
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