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If A=[a(ij)](mxxn) is a matrix and B is ...

If `A=[a_(ij)]_(mxxn)` is a matrix and B is a non-singular square submatrix of order r, 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-MATRICES-Exercise
  1. IfA=[a(ij)](mxxn) is a matrix of rank r and B is a square submatrix of...

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  2. The rank of a null matrix is

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  3. If A=[a(ij)](mxxn) is a matrix and B is a non-singular square submatri...

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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| = |A|^(...

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  10. Let A=[a(ij)](nxxn) be a square matrix of order 3 such that |A|=-7 an...

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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)=

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  20. Let {:A=[(a,0,0),(0,a,0),(0,0,a)]:}, then A^n is equal to

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