Home
Class 12
MATHS
The rank of the matrix [[-1,2,5],[2,-4,a...

The rank of the matrix `[[-1,2,5],[2,-4,a-4],[1,-2,a+1]]` is (where a = - 6)

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
A
Let `A = [[-1,2,5],[2,-4,-10],[1,-2,-5]]` `[because a = -6]`
Applying `R_(2) rarr R_(2) + 2R_(1) and R_(3)rarr R_(3) + R_(1)` then
`A = [[-1,2,5],[0,0,0],[0,0,0]] rArr p (A) =1`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|16 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise For Session 4|9 Videos

  • MATHEMATICAL INDUCTION

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

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|31 Videos

Similar Questions

Explore conceptually related problems

If the rank of the matrix [[-1,2,5],[2,-4,a-4],[1,-2,a+1]] is 1 then the value of a is (A) -1 (B) 2 (C) -6 (D) 4

Find adjoint of the matrix: [[1,2],[3,4]

show that the matrix A=[(2,-2,-4),(-1,3,4),(1,-2,-3)] is idempotent.

Express the matrix [[5,1,-1],[2,-3,4],[7,1,-3]] as a sum of symmetric and skew symmetric matrix

Find the adjoint of matrix [(2,3),(1,4)]

Show that the matrix A = [[1,-1,5],[-1,2,1],[5,1,3]] is a symmetric matrix.

For the matrix ( A=[[-3,6,0],[4,-5,8],[0,-7,-2]] ), find ( 1/2(A-A') ), where A' is the transpose of matrix A.

Find the transpose of the following matrix: [[-1,5,6],[sqrt3,5,6],[2,3,-1]]

If matrix A = [[1,2,3],[2,5,7],[-2,-4,-5]] , Then find A^-1 using elementary transformations (row or column).

ARIHANT MATHS-MATRICES -Exercise (Single Option Correct Type Questions)
  1. If a square matrix A is involutory, then A^(2n+1) is equal to:

    Text Solution

    |

  2. If A=[[cos theta,sin theta],[-sin theta,cos theta]], then lim (n rarr...

    Text Solution

    |

  3. The rank of the matrix [[-1,2,5],[2,-4,a-4],[1,-2,a+1]] is (where a = ...

    Text Solution

    |

  4. A is an involutory matrix given by A=[{:(0,1,-1),(4,-3,4),(3,-3,4):}]t...

    Text Solution

    |

  5. Let A be an nth-order square matrix and B be its adjoint, then |A B+K ...

    Text Solution

    |

  6. If A and B are two square matrices such that B=-A^(-1)BA, then (A+B)^(...

    Text Solution

    |

  7. If matrix A=[a(ij)](3xx), matrix B=[b(ij)](3xx3), where a(ij)+a(ji)=0 ...

    Text Solution

    |

  8. Let A be a nxxn matrix such thatA ^(n) = alpha A, where alpha is a ...

    Text Solution

    |

  9. If A=[[(-1+isqrt(3))/(2i),(-1-isqrt(3))/(2i)],[(1+isqrt(3))/(2i),(1-is...

    Text Solution

    |

  10. The number of 2x2 matrices X satisfying the matrix equation X^2=I(Ii s...

    Text Solution

    |

  11. if A and B are squares matrices such that A^(2006)=O and A B=A+B , the...

    Text Solution

    |

  12. Prove that: 2cos frac (pi)(13)cos frac (9pi)(13)+cos frac (3pi)(13)+co...

    Text Solution

    |

  13. There are two possible values of A in the solution of the matrix equ...

    Text Solution

    |

  14. If f (theta) = [[cos^(2) theta , cos theta sin theta,-sin theta],[cos ...

    Text Solution

    |

  15. In a square matrix A of order 3 the elements a(ii) 's are the sum of...

    Text Solution

    |

  16. If Aa n dB are two non-singular matrices of the same order such that B...

    Text Solution

    |

  17. If A=[[cos theta , sin theta],[sin theta,-costheta]], B = [[1,0],[-1,1...

    Text Solution

    |

  18. If A is a square matrix of order 3 such that abs(A)=2, then abs((adj...

    Text Solution

    |

  19. If A and B are different matrices satisfying A^(3) = B^(3) and A^(2)...

    Text Solution

    |

  20. Show that A is a symmetric matrix if A= [ (1,0), (0, -1)]

    Text Solution

    |