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 somerxrsubmatrix with a nonzero determinant, and all square submatrices of larger sizehave 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- 13 0A =6.10 0- 136 0rank (A) = i

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arious advanced texts in linear algebra prove the following determinant criterion for rank: he rank of a matrix A is rif and only if A has some rxr submatrix with a nonzero determinant, and all square submatrices of larger size ave 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.) Ise this criterion to find the rank of the matrix. 1 -1 3 0 A = 6 1 0 0 -1 3 6 0 ank (A) = i

arious advanced texts in linear algebra prove the following determinant criterion for rank: he rank of a matrix A is rif and only if A has some rxr submatrix with a nonzero determinant, and all square submatrices of larger size ave 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.) Ise this criterion to find the rank of the matrix. 1 -1 3 0 A = 6 1 0 0 -1 3 6 0 ank (A) = i

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

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 somerxrsubmatrix 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
- 1
3 0
A =
6.
1
0 0
- 1
3
6 0
rank (A) = i

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