Home
Class 11
MATHS
The rank of the matrix {:A=[(1,2,3),(4,5...

The rank of the matrix `{:A=[(1,2,3),(4,5,6),(3,4,5)]:}` is

Text Solution

Verified by Experts

The correct Answer is:
2
We have,
`{:absA=abs((1,2,3),(4,5,6),(3,4,5)):}=1(25-24)-2(20-18)+3(16-15)=0`
Therefore, r(A) is less than 3.
We observe that `{:[(5,6),(4,5)]:}` is a non-singular square submatrix of order 2. Hence, r (A) =2.
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    OBJECTIVE RD SHARMA|Exercise Section I - Solved Mcqs|57 Videos

  • MATRICES

    OBJECTIVE RD SHARMA|Exercise Section I - Assertion Reason Type|12 Videos

  • LOGARITHMS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|21 Videos

  • MEAN VALUE THEOREMS

    OBJECTIVE RD SHARMA|Exercise Exercise|28 Videos

Similar Questions

Explore conceptually related problems

The rank of the matrix A={:[(1,2,3),(3,6,9),(1,2,3)]:} , is

The rank of the matrix A=[[-1,2,3-2,4,6]] is

The rank of the matrix A={:[(1,2,3,4),(4,3,2,1)]:} , is

The order of the matrix [{:(1,2,3),(4,5,6):}] is

The element in the second row and third column of the matrix [{:(1,2,3),(4,5,6),(7,8,9):}] is ________

The rank of the matrix {:[(1,2,3,0),(2,4,3,2),(3,2,1,3),(6,8,7,5)]:} , is

If the rank of the matrix A= [(1,2,3,0),(2,4,3,2),(3,2,1,3),(6,8,7,alpha)] is 3 then a= (A) -5 (B) 5 (C) 4 (D) 4

The number of column of the matrix [{:(1,2,3),(4,5,6):}] is ________

The rank of the matrix [{:(-1,2,5),(2,-4,a-4),(1,-2,a+1):}] is

OBJECTIVE RD SHARMA-MATRICES-Chapter Test
  1. The rank of the matrix {:A=[(1,2,3),(4,5,6),(3,4,5)]:} is

    Text Solution

    |

  2. If A is an invertible matrix and B is a matrix, then

    Text Solution

    |

  3. What is the order of the product [x" "y" "z][{:(a,h,g),(h,b,f),(g,f,c)...

    Text Solution

    |

  4. If {:A=[(a,0,0),(0,b,0),(0,0,c)]:}," then "A^(-1), is

    Text Solution

    |

  5. The inverse of the matrix {:[(1,3),(3,10)]:} is equal to

    Text Solution

    |

  6. If {:A=[(5,2),(3,1)]:}," then "A^(-1)=

    Text Solution

    |

  7. If {:X=[(3,-4),(1,-1)]:}, the value of X^n is equal to

    Text Solution

    |

  8. If {:A=[(5,2),(3,1)]:}," then "A^(-1)=

    Text Solution

    |

  9. For the system of equaltions : x+2y+3z=1 2x+y+3z=2 5x+5y+9z=4

    Text Solution

    |

  10. If {:A=[(3,1),(-1,2)]:}," then "A^(-2)=

    Text Solution

    |

  11. if |[4,x+2],[2x-3,x+1]| is a symmetric then x=

    Text Solution

    |

  12. If {:A+B=[(1,0),(1,1)]andA-2B=[(-1,1),(0,-1)]:}," then "A=

    Text Solution

    |

  13. {:[(-6,5),(-7,6)]^(-1)=:}

    Text Solution

    |

  14. From the matrix equation AB = AC we can conclude B = C provided that

    Text Solution

    |

  15. If I3 is the identily matrix of order 3, then (I3)^(-1)=

    Text Solution

    |

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

    Text Solution

    |

  17. If A and B are two matrices such that A+B and AB are both defind, then

    Text Solution

    |

  18. A and B are tow square matrices of same order and A' denotes the tran...

    Text Solution

    |

  19. Consider the system of equations a1x+b1y+c1z=0 a2x+b2y+c2z=0 a3...

    Text Solution

    |

  20. The system of linear equations x+y+z=2 2x+y-z=3 3x+2y+kz=4 has a...

    Text Solution

    |

  21. If A and B are square matrices of order 3 such that absA=-1,absB=3," t...

    Text Solution

    |