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If A is a matrix such that there exists ...

If A is a matrix such that there exists a square submatrix of order r which is non-singular and eveny square submatrix or order r + 1 or more is singular, then

A

rank of A is r

B

rank of A is greater than r

C

rank of A is less than r

D

none of these

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-MATRICES-Exercise
  1. A=[a(ij)](mxxn) is a square matrix, if

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  2. The rank of a null matrix is

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  3. If A is a matrix such that there exists a square submatrix of order r ...

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  4. Which of the following is correct ?

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  5. If a square matrix A is orthogonal as well as symmetric, then

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  6. Let A be a skew-symmetric of odd order, then absA is equal to

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  7. Let A be a skew-symmetric matrix of even order, then absA

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  8. If A is an orthogonal matrix, then

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  9. Let A be a non-singular square matrix of order n. Then; |adjA| =

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  10. Let A=[a(ij)](n xxn) be a square matrix and let c(ij) be cofactor of...

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  11. If A is a non-singlular square matrix of order n, then the rank of A i...

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  12. If A is a matrix such that there exists a square submatrix of order r ...

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  13. Let A be a matrix of rank r. Then,

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  14. Let A=[a(ij)](mxxn) be a matrix such that a(ij)=1 for all I,j. Then ,

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  15. If A is a non-zero column matrix of order mxx1 and B is a non-zero row...

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  16. The rank of the matrix {:[(1,2,3,0),(2,4,3,2),(3,2,1,3),(6,8,7,5)]:}, ...

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  17. If A is an invertible matrix, then "det" (A -1) is equal to

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  18. If A and B are two matrices such that rank of A = m and rank of B = n...

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  19. If A=[3 4 2 4] , B=[-2-2 0-1] , then (A+B)^(-1) (a) is a skew-symmetr...

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  20. Let A=[a0 0 0a0 0 0a] , then A^n is equal to [a^n0 0 0a^n0 0 0a] (b) [...

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