Home
Class 12
MATHS
Find minors and cofactors of the element...

Find minors and cofactors of the elements `a_(11), a_(21)` in the determinant `Delta=|(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(23))|`

Text Solution

Verified by Experts

by the definition of minor and cofactors
we have
Minor of `a_11 = M_11 = [[a_22,a_23],[a_32,a_33]]`
= `a_22. a_33 - a_23. a_32`
Cofactor of `a_11 = A_11 = (-1)^(1+1) M_11 = a_22. a_33 - a_23. a_32`
Minor of `a_21 = M_21 = [[a_12,a_13],[a_32,a_33]] = a_12.a_33 - a_31.a_32`
...
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    NCERT|Exercise MISCELLANEOUS EXERCISE|19 Videos
  • DETERMINANTS

    NCERT|Exercise EXERCISE 4.4|5 Videos
  • DETERMINANTS

    NCERT|Exercise EXERCISE 4.6|15 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    NCERT|Exercise QUESTION|3 Videos
  • DIFFERENTIAL EQUATIONS

    NCERT|Exercise EXERCISE 9.1|12 Videos

Similar Questions

Explore conceptually related problems

Find the minors and cofactors of the elements of the determinant Delta = |{:(a_(11), a_(12), a_(13)), (a_(21), a_(22), a_(23)), (a_(31), a_(32), a_(33)):}|

Let A=[a_("ij")]_(3xx3) be a matrix such that A A^(T)=4I and a_("ij")+2c_("ij")=0 , where C_("ij") is the cofactor of a_("ij") and I is the unit matrix of order 3. |(a_(11)+4,a_(12),a_(13)),(a_(21),a_(22)+4,a_(23)),(a_(31),a_(32),a_(33)+4)|+5 lambda|(a_(11)+1,a_(12),a_(13)),(a_(21),a_(22)+1,a_(23)),(a_(31),a_(32),a_(33)+1)|=0 then the value of lambda is

Find minors and cofactors of the elements of the determinant det[[2,-3,56,0,41,5,-7]]a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33)=0

(a_(1))/(a_(1)+a_(2))+(a_(3))/(a_(3)+a_(4))=(2a_(2))/(a_(2)+a_(3))

Let A=[a_(ij)]_(3xx3) be a matrix such that A.A^(T)=4I and a_(ij)+2c_(ij)=0 where c_(ij) is the cofactor of a_(ij) AAi & j , I is the unit matrix of order 3 and A^(T) is the transpose of the matrix A If |(a_(11)+4,a_(12), a_(3)),(a_(21),a_(22)+4,a_(24)),(a_(31),a_(32),a_(33)+4)|+5lamda|(a_(11)+1,a_(12),a_(13)),(a_(21),a_(22)+1,a_(23)),(a_(31),a_(32),a_(33)+1)|=0 then lamda=a/b where a and b are coprime positive integers then the value of a+b is______

Find minors and co-factors of the elements of the determinant : |{:(2,-3,5),(6,0,4),(1,5,-7):}| and verify that a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33)=0

If matrix [(1,2,-1),(3,4,5),(2,6,7)] and its inverse is denoted by A^(-1)=[(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33))] value of a_(32)=

Let A=[a_(ij)]_(3xx3) be a square matrix such that A A^(T)=4I, |A| lt 0 . If |(a_(11)+4,a_(12),a_(13)),(a_(21),a_(22)+4,a_(23)),(a_(31),a_(32),a_(33)+4)|=5lambda|A+I|. Then lambda is equal to

Let A=[a_(ij)]_(3xx3) be a matrix such that A A^T=4T and a_(ij)+2c_(ij)=0 , where c_(ij) is the cofactor of a_(ij) and I is the unit matrix of order 3 . |(a_11 +4 , a_12 , a_13),(a_21 , a_(22)+4 ,a_23),(a_31,a_32,a_(33)+4)|+5lambda|(a_(11)+1 , a_12,a_13),(a_21,a_(22)+1, a_23),(a_31, a_32 , a_(33)+1)|=0 then the value of 10lambda is ____

NCERT-DETERMINANTS-SOLVED EXAMPLES
  1. Find the area of the triangle whose vertices are (3, 8),(-4, 2)and (5,...

    Text Solution

    |

  2. Prove that |b+c a a b c+a b cc a+b|=4a b c

    Text Solution

    |

  3. If x, y, z are different and Delta=|[x,x^2, 1+x^3],[y, y^2,1+y^3],[z, ...

    Text Solution

    |

  4. Find the equation of the line joining A( 1,3) and B (0,0) using deter...

    Text Solution

    |

  5. Find the minor of element 6 in the determinant Delta=|[1, 2, 3],[ 4, 5...

    Text Solution

    |

  6. The sum of three numbers is 6. If we multiply third number by 3 and a...

    Text Solution

    |

  7. Solve the following system of equations by matrix method. 3x-2y + 3z=...

    Text Solution

    |

  8. Solve the system of equations 2x + 5y = 1 and 3x + 2y = 7.

    Text Solution

    |

  9. Show that the matrix A=[[2,3],[ 1,2]]satisfies the equation A^2-4A+I=...

    Text Solution

    |

  10. If A=[(2,3),(1,-4)]and B=[(1,-2),(-1, 3)], then verify that (A B)^(-1)...

    Text Solution

    |

  11. If A=[[1 ,3 ,3],[ 1, 4 ,3],[ 1, 3, 4]],then verify thatA a d j A = |A|...

    Text Solution

    |

  12. Find adj for A=[[1 ,2],[ 3 ,4]]

    Text Solution

    |

  13. Find minors and cofactors of the elements of the determinant|[2,-3, 5...

    Text Solution

    |

  14. Find minors and cofactors of the elements a(11), a(21) in the determi...

    Text Solution

    |

  15. Find minors and cofactors of all the elements of the determinant |[1,...

    Text Solution

    |

  16. If a, b, c are positive and unequal, show that value of the determina...

    Text Solution

    |

  17. If a,b,c are in A.P, find value of |[2y+4,5y+7,8y+a],[3y+5,6y+8,9y+b],...

    Text Solution

    |

  18. Show that Delta=|((y+z)^2,xy,zx),(xy,(x+z)^2,yz),(xz,yz,(x+y)^2)|=2xyz...

    Text Solution

    |

  19. Use product [1-1 2 0 2-3 3-2 4][-2 0 1 9 2-3 6 1-2]to solve the syste...

    Text Solution

    |

  20. Prove that Delta=|[a+bx, c+dx, p+qx],[ax+b, cx+d, px+q],[u ,v, w]|=(1-...

    Text Solution

    |