In advanced linear algebra, one proves the following determinant criterion for rank: The rank of a matrix A is r if and only if A has some r × r submatrix with a nonzero determinant, and all square submatrices of larger size have determinant zero. (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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