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The number of 3xx3 matrices a whose entr...

The number of `3xx3` matrices a whose entries are either 0 or 1 and for which the system `A [(x),(y),(z)]=[(1),(0),(0)]` has exactly two distinct solutions is

A

o

B

`2^(9) -1`

C

168

D

2

Text Solution

Verified by Experts

The correct Answer is:
A
Three planes cannot meet only at two distinect points.
Hence. Number of matrices = 0
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ARIHANT MATHS ENGLISH-MATRICES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

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  2. Let A be a 2xx2 matrix Statement -1 adj (adjA)=A Statement-2 abs(a...

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  3. The number of 3xx3 matrices a whose entries are either 0 or 1 and for ...

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  4. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

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  5. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

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  6. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

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

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

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

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

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

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

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

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

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

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

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

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

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