Solved: Various advanced texts in linear algebra prove the following determinant
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 r r 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. (a) 120 2 4 1 (b) 123 246 (c) 101 2 1 3 3 1 4 (d) 1 120 3100 1240
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