Home
Class 12
MATHS
Let A =[(1,-1,1),(2,1,-3),(1,1,1)] an...

Let `A =[(1,-1,1),(2,1,-3),(1,1,1)]` and `10B=[(4,2,2),(-5,0,alpha),(1,-2,3)]`. If B is the inverse of A, then `alpha` is :

A

2

B

0

C

5

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
Since B is the inverse of A i.e. `B=A^(-1)`
So, `10A^(-1)=[(4,2,2),(-5,0,alpha),(1,-2,3)]`
`implies10A^(-1)A=[(4,2,2),(-5,0,alpha),(1,-2,3)]A`
`=10l=[(4,2,2),(-5,0,alpha),(1,-2,3)][(1,-1,1),(2,1,-3),(1,1,1)]`
`implies[(10,0,0),(0,10,0),(0,0,10)]=[(10,0,0),(-5+alpha, 5+alpha, -5+alpha),(0,0,10)]`
`implies -5+alpha=0impliesalpha=5`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|18 Videos

  • MATRICES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|18 Videos

  • MATHEMATICAL LOGIC

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|22 Videos

  • MHTCET 2007

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MATHEMATICS|50 Videos

Similar Questions

Explore conceptually related problems

Let A=[(1,-1,1),(2,1,-3),(1,1,1)] and B=[(4,2,2),(-5,0,alpha),(1,-2,3)] If B is the inverse of matrix A , then alpha= (A) 2 (B) -2 (C) 5 (D) -5

Let A+2B=[(1,2,0),(6,-1,3),(-5,3,1)] and 2A-B=[(2,-1,5),(2,-1,6),(0,1,2)], then find tr(A)-tr(B).

Let A+2B={:[(3,2,-3),(1,0,4),(3,1,2)]:}and-A-B={:[(1,0,3),(-1,4,1),(3,2,1)]:} . Find A and B.

If A=[(1,0),(3,-1),(-5,2)] and B=[(1,-2),(-2,2),(1,1)] , then find the matrix 'X' such that 3A + X = 5B.

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-MATRICES-MISCELLANEOUS PROBLEMS
  1. If A is a non-singular matrix of order 3, then adj(adj(A)) is equal to

    Text Solution

    |

  2. Let {:A=[(1,2),(-5,1)]and A^(-1)=xA+yI:}, then the values of x and y a...

    Text Solution

    |

  3. Let A =[(1,-1,1),(2,1,-3),(1,1,1)] and 10B=[(4,2,2),(-5,0,alpha),(...

    Text Solution

    |

  4. If A(theta)=[(1, than theta),(-tan, theta=1)] and AB=l, then (sec^(2)t...

    Text Solution

    |

  5. If A=[(cos alpha, -sin alpha, 0),(sin alpha, cos alpha,0),(0,0,1)] the...

    Text Solution

    |

  6. Suppose A is a matrix of order 3 and B=|A|A^(-1). If |A|=5, then |B| i...

    Text Solution

    |

  7. if[{:(2,1),(3,2):}]A[{:(-3,2),(5,-3):}]=[{:(1,0),(0,1):}],"then" A=?

    Text Solution

    |

  8. If f(theta)=[(cos theta, -sin theta,0),(sin theta, cos theta, 0),(0,0,...

    Text Solution

    |

  9. If A is a singular matrix, then Aadj(A) is a/an

    Text Solution

    |

  10. If k is a scalar and l is a unit matrix of order 3 then adj(kl) is equ...

    Text Solution

    |

  11. Consider the system of equations x+y+z=6 x+2y+3z=10 x+2y+lambda...

    Text Solution

    |

  12. Let a, b, c be any real numbers. Suppose that there are real numbers...

    Text Solution

    |

  13. Let a, b, c be positive real numbers. The following system of equation...

    Text Solution

    |

  14. If the system of linear equations x+2ay +az =0,x+3by+bz =0 and x+4cy ...

    Text Solution

    |

  15. The symmetric part of the matrix A=[(1,2,4),(6,8,2),(2,-2,7)] is equal...

    Text Solution

    |

  16. If {:A=[(1,0,0),(0,1,0),(a,b,-1)]:}, then A^2 is equal to

    Text Solution

    |

  17. If A=[1 2 2 2 1-2a2b] is a matrix satisfying the equation AA^T=""9I , ...

    Text Solution

    |

  18. If A is a 3xx3 such that |5.adj(A)|=5 then |A| is equal to

    Text Solution

    |

  19. If A=[(alpha, 2),(2, alpha)] and |A^(3)|=27 then alpha is equal to

    Text Solution

    |

  20. The elements in the first row and third column of the inverse of the m...

    Text Solution

    |