Home
Class 12
MATHS
Write the minors and cofactors of eac...

Write the minors and cofactors of each element of the first column of the following matrices and hence evaluate the determinant in each case: `A=[0 2 6 1 5 0 3 7 1]` (ii) `A=[a hgh bfgfc]` (ii) `A=[2-1\ \ 0-3\ 0\ \ 1 1\ 1-1\ 2\ \ -1\ \ \ 5\ \ \ \ \ \ \ 1\ \ \ -2\ \ \ \ \ \ 1\ \ \ \ \ \ 0]`

Text Solution

Verified by Experts

`A=[(0,2, 6),( 1,5, 0),( 3, 7, 1)]`
`M_(11)=5-7xx0=5`
`M_(21)=2-7xx6=-40`
`M_(31)=2xx0-5xx6=-30`
`C_(11)=(-1)^2 M_(11)=5`
`C_(21)=(-1)^3 M_(21)=40`
`C_(31)=(-1)^4 M_(31)=-30`
`|A|= a_(11) c_(11)+a_(21) c_(21)+a_(31) c_(31)`
...
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos
  • DIFFERENTIABILITY

    RD SHARMA|Exercise Solved Examples And Exercises|136 Videos

Similar Questions

Explore conceptually related problems

Write the minors and cofactors of each element of the first column of the following matrices and hence evaluate the determinant in each case: A=[5200-1] (ii) A=[-1423]( iii) A=[1-324-12352] (iv) A=[1abc1bca1cab]

Write the minor and cofactor of each element of the following determinants and also evaluate the determinant in each case: |[1,0,0],[0,1,0],[0,0,1]|

Write the minor and cofactor of each element of the following determinants and also evaluate the determinant in each case: |[1,3,-2],[4,-5,6],[3,5,2]|

Write the minor and cofactor of each element of the following determinants and also evaluate the determinant in each case: |[5,-10],[0,3]|

Write the minors and co-factors of each elements of the first column of the matrix A A=[(1,-3,2),(4,-1,2),(3,5,2)]

Write the minor and cofactor of each element of second column in the following determinants and evaluate them: |[1,2,4],[1,3,9],[1,4,16]|

Write down the co-factors of the elements of the first row of the following determinant and hence evaluate the determinant |{:(1,3,-3),(2,-1,0),(4,-2,5):}|

Find the minor and cor-factor of each element of the first column of the following determinants : |{:(0,2,6),(1,5,0),(3,7,1):}| Hence or otherwise evaluate them.

Find the minors and cofactors of the elements of the following determinants: abs([1,0,4],[3,5,-1],[0,0,2])

Find the minors and cofactors of the elements of the following determinants: abs([2,-3,5],[6,0,4],[1,5,-7])

RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. Prove that the determinant |(x,sin theta,cos theta),(-sin theta,-x,1),...

    Text Solution

    |

  2. Write the minors and cofactors of each element of the first column ...

    Text Solution

    |

  3. Write the minors and cofactors of each element of the first column ...

    Text Solution

    |

  4. Evaluate the following determinants: |x-7x5x+1| (ii) |costheta-sin...

    Text Solution

    |

  5. Evaluate the following determinants: |x-7x5x+1| (ii) |costheta-sin...

    Text Solution

    |

  6. Evaluate: |2 3 7 13 17 5 15 20 12|^2 .

    Text Solution

    |

  7. Show that |sin10o-cos10osin80ocos80o|=1

    Text Solution

    |

  8. Evaluate |2 3-5 7 1-2-3 4 1| by two methods.

    Text Solution

    |

  9. Evaluate: =|0sinalpha-cosalpha-sinalpha0sinbetacosalpha-sinbeta0|

    Text Solution

    |

  10. Evaluate: =|cosalphacosbetacosalphasinbeta-sinalpha-sinbetacosbeta0sin...

    Text Solution

    |

  11. If A=[2 5 2 1] and B=[4-3 2 5] , verify that |A B|=|A||B| .

    Text Solution

    |

  12. If A=[[1 ,0 ,1],[0 ,1, 2],[ 0, 0, 4]] , then show that |3A|" "=" "27|...

    Text Solution

    |

  13. Find the values of x , if |2 4 5 1|=|2x4 6x| (ii)|2 3 4 5|=|x3 2x5| (...

    Text Solution

    |

  14. Find the values of x , if |3x7 2 4|=10 (ii) |x+1x-1x-3x+2|=|4-1 1 3| ...

    Text Solution

    |

  15. Find the integral value of x , if |[x^2,x,1],[ 0, 2, 1],[ 3, 1, 4]...

    Text Solution

    |

  16. For what value of x the matrix A is singular? A=[1+x7 3-x8] (ii) A=[x-...

    Text Solution

    |

  17. Without expanding evaluate the determinant |41 1 5 79 7 9 29 5 3| .

    Text Solution

    |

  18. If w is a complex cube root of unity. Show that |1w w^2w w^2 1w^2 1...

    Text Solution

    |

  19. Show that |1a b+c1b c+a1c a+b|=0 .

    Text Solution

    |

  20. Show that |[b-c,c-a, a-b],[ c-a, a-b,b-c],[ a-b,b-c,c-a]| = 0 .

    Text Solution

    |