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. (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.) Use this criterion to find the rank of the matrix. 1 6 5 30 -1| rank (A) =
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. (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.) Use this criterion to find the rank of the matrix. 1 6 5 30 -1| rank (A) =
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter11: Matrices And Determinants
Section11.CR: Chapter Review
Problem 11CC
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![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.
(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.)
Use this criterion to find the rank of the matrix.
16
5 30 -1
rank (A) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F080b5c0e-ffcb-4ace-82d3-1f50cc9b6c52%2F8a460678-a037-4558-b142-ab8e291da256%2Fmmez2mf_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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.
(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.)
Use this criterion to find the rank of the matrix.
16
5 30 -1
rank (A) =
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