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The number of 3 x 3 non-singular matrice...

The number of 3 x 3 non-singular matrices, with four entries as 1 and all other entries as 0, is:- (1) 5 (2) 6 (3) at least 7 (4) less than 4

A

5

B

6

C

atleast 7

D

less then 4

Text Solution

Verified by Experts

The correct Answer is:
C
First row with exactly one zero
`therefore ` Total number of cases = 6
First row 2 zeroes, we get more cases.
`therefore ` Total we get more then 7.
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ARIHANT MATHS ENGLISH-MATRICES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

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  2. Let K be a positive real number and A=[(2k-1,2sqrt(k),2sqrt(k)),(2sqrt...

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  3. The number of 3 x 3 non-singular matrices, with four entries as 1 and ...

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  4. Let a be a 2xx2 matrix with non-zero entries and let A^(2)=I, where I ...

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  5. Let M and N be two 3xx3 nonsingular skew-symmetric matrices such that ...

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  6. Let a, b, and c be three real numbers satifying [(a, b, c)] [(1,9,7)...

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  7. Let a, b, and c be three real numbers satifying [(a, b, c)] [(1,9,7)...

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  8. Let a, b, and c be three real numbers satifying [(a, b, c)] [(1,9,7)...

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  9. Let omega!=1 be cube root of unity and S be the set of all non-singula...

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  10. Let M be a 3xx3 matrix satisfying M[0 1 0]=M[1-1 0]=[1 1-1],a n dM[1 1...

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  11. Let A and B two symmetric matrices of order 3. Statement 1 : A(BA) a...

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  12. Let P=[a(i j)] be a 3xx3 matrix and let Q=[b(i j)],w h e r eb(i j)=2^(...

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  13. If P is a 3xx3 matrix such that P^T = 2P+I, where P^T is the transpose...

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  14. If the adjoint of a 3x3 matrix P is (1 4 4) (2 1 7) (1 1 3) , t...

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  15. Let A=((1,0,0),(2,1,0),(3,2,1)). If u(1) and u(2) are column matrices ...

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  16. Let P and Q be 3xx3 matrices P ne Q. If P^(3)=Q^(3) and P^(2)Q=Q^(2)P,...

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  17. IF P=[(1,alpha,3),(1,3,3),(2,4,4)] is the adjoint of 3xx3 matrix A and...

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  18. For 3xx3 matrices M \ a n d \ N , which of the following statement (s)...

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  19. Let omega be a complex cube root of unity with omega!=1a n dP=[p(i j)]...

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  20. If A is an 3xx3 non-singular matrix such that A A^T=A^TA and B=A^(-1)A...

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