Home
Class 12
MATHS
If A(0) = [[2 ,-2,-4],[-1,3,4],[1,-2,-3]...

If `A_(0) = [[2 ,-2,-4],[-1,3,4],[1,-2,-3]] and B_(0)= [[-4,-4,-4],[1,0,1],[4,4,3]]` then find `A_0-B_O`

A

unique solution

B

infinite solution

C

finitrly many solution

D

no solution

Text Solution

Verified by Experts

The correct Answer is:
D
`because A_(0) = [[2,-2,-4],[-1,3,4],[1,-2,-3]] rArr abs(A_(0)) = 0`
and abj `B_(0) = [[-4,1,4],[-3,0,4],[-3,1,-3]]^(T) = [[-4,-3,-3],[1,0,1],[4,4,3]]=B_(0) `
`because B_(n) = adj (B_(n-1)), n in N `
`therefore B_(1) = adj (B_(0) )=B_(0)`
`rArr B_(2) = adj (B_(1)) = adj (B_(0)) = B_(0),`
`B_(3) = B_(0) , B_(4) = B_(0) , ...`
`therefore B_(n) = B_(0) AA n in N`
`because abs(A_(0)) = 0`
`rArr A_(0)^(-1)` is not possible
Hence, System of equation `A_(0) X = B_(0)` has no Sol.
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|9 Videos

  • MATRICES

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 2|19 Videos

  • MATHEMATICAL INDUCTION

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|29 Videos

Similar Questions

Explore conceptually related problems

If A_(0) = [[2 ,-2,-4],[-1,3,4],[1,-2,-3]] and B_(0) [[-4,-4,-4],[1,0,1],[4,4,3]] then find A_0 +B_0

If A = [[-1, 2 ,3],[-1, 0, 2],[1, -3, 1]] and B = [[4,5,6],[-1, 0, 1], [2,1,2]], find 4A-3B

If A=[[3,-3,4],[2,-3,4],[0,-1,1]] , then

If A=(a_(i j))= [[2, 3,-5],[1, 4, 9],[ 0, 7,-2]] and B=(b_(i j))=[[2, 1,-1],[-3, 4, 4],[ 1, 5, 2]], then find a_(22)+b_(21)

If A=[(2,-2,-4),(-1,3,4),(1,-2,-3)] and B=[(-4,-3,-3),(1,0,1),(4,4,3)] are two matrices, then the value of the determinant (A+A^(2)B^(2)+A^(3)+A^(4)B^(4)+"………"20" terms")

If A= [[1,-1,0],[2,3,4],[0,1,2]] and B = [[2,2,-4],[-4,2,-4],[2,-1,5]] then, (A) A^(-1) =B (B) A^(-1) =6B (C) B^(-1) =B (D) B^(-1) = 1/6 A

If A=[[2,1],[3,0],[5,1]] and B = [[4,0],[3,8]] then find AB

if A = [[3,9,0],[1,8,-2]] and B = [[4,0,2],[7,1,4]] find A+B and A-B?

If A=[[1,2,3],[2,0,-2]],B=[[1,1,-1],[2,0,3],[3,-1,2]] and C=[[1,3],[0,2],[-1,4]] find A(BC).

If A=[[3, -1, 4], [2, 3, 1]], B=[[1, 3, 4], [2, 1, 0], [-3, 2, 3]] find AB

ARIHANT MATHS ENGLISH-MATRICES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. If A(0) = [[2 ,-2,-4],[-1,3,4],[1,-2,-3]] and B(0)= [[-4,-4,-4],[1,0,1...

    Text Solution

    |

  2. Let A=[(1,0,0),(0,1,1),(0,-2,4)],I=[(1,0,0),(0,1,0),(0,0,1)] and A^-1=...

    Text Solution

    |

  3. about to only mathematics

    Text Solution

    |

  4. If A=[(1,0),(1,1)] and I=[(1,0),(0,1)] then which one of the following...

    Text Solution

    |

  5. If A^(2)-A+I=O, then A^(-1) is equal to

    Text Solution

    |

  6. Let {:A=[(1,0,0),(2,1,0),(3,2,1)]:}and U1,U2,U3 be column matrices sat...

    Text Solution

    |

  7. Let A = [(1,0,0), (2,1,0), (3,2,1)], and U1, U2 and U3 are columns of ...

    Text Solution

    |

  8. If A= ((1,0,0),(2,1,0),(3,2,1)), U(1), U(2), and U(3) are column matri...

    Text Solution

    |

  9. Let A=[{:(1,2),(3,4):}]and B = [{:(a,0),(0,b):}] where a, b are natura...

    Text Solution

    |

  10. If A and B are square matrices of size nxxn such that A^2-B^2 = (A-B)(...

    Text Solution

    |

  11. Let A= [[5,5alpha,alpha],[0,alpha,5alpha],[0,0,5]] . If |A^2|...

    Text Solution

    |

  12. Let A and B be 3xx3 matrtices of real numbers, where A is symmetric, "...

    Text Solution

    |

  13. Let A be a square matrix all of whose entries are integers. Then wh...

    Text Solution

    |

  14. Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identi...

    Text Solution

    |

  15. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

    Text Solution

    |

  16. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

    Text Solution

    |

  17. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |