Home
Class 11
MATHS
Let A=|(a(1),b(1),c(1)),(a(2),b(2),c(2))...

Let A=`|(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3)c_(3))|`then the cofactor of `a_(31)`is:

A

`b_(1)c_(2)+b_(2)c_(1)`

B

`b_(1)b_(2)-c_(1)c_(2)`

C

`b_(1)c_(2)-b_(2)c_(1)`

D

`b_(2)c_(1)-b_(1)c_(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MATRICES AND DETERMINANTS

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE (ANSWER THE FOLLOWING QUESTIONS)|18 Videos

  • INTRODUCTION TO PROBABILITY THEORY

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE (Choose the correct option for the following)|39 Videos

  • SETS,RELATIONS AND FUNCATIONS

    PREMIERS PUBLISHERS|Exercise II. Choose the correct option for the following. (M.C.Q)|35 Videos

Similar Questions

Explore conceptually related problems

If A_(i),B_(i),C_(i) are the cofactors of a_(i),b_(i),c_(i) respectively,i=1,2,3 in Delta =|(a_(1),b_(2),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))| show that |(A_(1),B_(1),C_(1)),(A_(2),B_(2),C_(2)),(A_(3),B_(3),C_(3))|=Delta^(0)

If A = [{:(3," "1,-1),(2,-2," "0),(1," "2,-1):}] "and"" "A^(-1)=[(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33))] then the value of a_(23) is

(a) If A=((4,2),(-1,x)) and such that (A-2I)(A-3I)=0. find the value of x. (b) If A_(i),B_i,C_(i) are the cofactors of a_(i),b_(i),c_(i) , respectively, i=1 to 3 in |A|=|(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(3)),(a_(3),b_(3),c_(3))| , show that |(A_(1),B_(1),C_(1)),(A_(2),B_(2),C_(2)),(A_(3),B_(3),C_(3))|=|A|^(2) .

if A_(1) ,B_(1),C_(1) ……. are respectively the cofactors of the elements a_(1) ,b_(1),c_(1)…… of the determinant Delta = |{:(a_(1),,b_(1),,c_(1)),(a_(2),,b_(2),,c_(2)),(a_(3),,b_(3),,c_(3)):}|, Delta ne 0 then the value of |{:(B_(2),,C_(2)),(B_(3),,C_(3)):}| is equal to

suppose D= |{:(a_(1),,b_(1),,c_(1)),(a_(2),,b_(2),,c_(2)),(a_(3),,b_(3),,c_(3)):}| and Dprime= |{:(a_(1)+pb_(1),,b_(1)+qc_(1),,c_(1)+ra_(1)),(a_(2)+pb_(2),,b_(2)+qc_(2),,c_(2)+ra_(2)),(a_(3)+pb_(3),,b_(3)+qc_(3),,c_(3)+ra_(3)):}| . Then

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

if (1+ax+bx^(2))^(4)=a_(0) +a_(1)x+a_(2)x^(2)+…..+a_(8)x^(8), where a,b,a_(0) ,a_(1)…….,a_(8) in R such that a_(0)+a_(1) +a_(2) ne 0 and |{:(a_(0),,a_(1),,a_(2)),(a_(1),,a_(2),,a_(0)),(a_(2),,a_(0),,a_(1)):}|=0 then the value of 5.(a)/(b) " is " "____"

if x,y and z are not all zero and connected by the equations a_(1)x+b_(1)y+c_(1)z=0,a_(z)x+b_(2)y+c_(2)z=0 and (p_(1)+lambdaq_(1))x+(p_(2)+lambdaq_(2))y+(p_(3)+lambdaq_(3))z=0 show that lambda =-|{:(a_(1),,b_(1),,c_(1)),(a_(2) ,,b_(2),,c_(2)),(p_(1) ,, p_(2),,p_(3)):}|-:|{:(a_(1),,b_(1),,c_(1)),(a_(2) ,,b_(2),,c_(2)),(q_(1) ,, q_(2),,q_(3)):}|

If a_(1) x^(3) + b_(1)x^(2) + c_(1)x + d_(1) = 0 and a_(2)x^(3) + b_(2)x^(2) + c_(2)x + d_(2) = 0 a pair of repeated roots common, then prove that |{:(3a_(1)", "2b_(1) ", "c_(1)),(3a_(2)", " 2b_(2)", "c_(1)),(a_(2)","b_(1)- a_(1)b_(2)", "c_(2)a_(1)-c_(2)a_(1)", "d_(1)a_(2)-d_(2)a_(1)):}|=0

PREMIERS PUBLISHERS-MATRICES AND DETERMINANTS-PROBLEMS FOR PRACTICE .(II CHOOSE THE CORRECT OPTION FROM THE FOLLOWING)
  1. If A is a square matrix such that A^(2)=A,then the value of A+(A-I)^(4...

    Text Solution

    |

  2. If A and B are symmetric matrices of same order than AB-BA is a:

    Text Solution

    |

  3. Let A=|(a(1),b(1),c(1)),(a(2),b(2),c(2)),(a(3),b(3)c(3))|then the cofa...

    Text Solution

    |

  4. The area of traingle whose vertices are (0,0),(3,4),and(2,5) is :

    Text Solution

    |

  5. Find the odd man out:

    Text Solution

    |

  6. Find the odd man out:

    Text Solution

    |

  7. Find the correct statement:

    Text Solution

    |

  8. Find the incorrect statement:

    Text Solution

    |

  9. Find the incorrect statement:

    Text Solution

    |

  10. Find the incorrect statement:

    Text Solution

    |

  11. The value|A|^(2)where |A|=|(2,5),(1,6)|is

    Text Solution

    |

  12. The minor of 7 in [(3,1,4),(-1,0,3),(6,7,5)]is

    Text Solution

    |

  13. If A=|(2,1),(1,2)|,B=|(2,4),(1,2)|then |AB| is

    Text Solution

    |

  14. If |(a(1),b(1),c(1)),(a(2),b(2),c(2)),(a(3),b(3),c(3))|is 8 the value ...

    Text Solution

    |

  15. Which one of the following is not true about the matrix [(2,0,0),(0,-2...

    Text Solution

    |

  16. Find which one is true. If A and B are two matrices such that A+B and ...

    Text Solution

    |

  17. If A is a square matrix then find the odd man out:

    Text Solution

    |

  18. If x(1), x(2), x(3) and y(1),y(2), y(3) are in arithmetic progression ...

    Text Solution

    |

  19. Let A andB be two skew symmetric matrices of the same order find the i...

    Text Solution

    |

  20. (i) If A and B are symmetric matrices of same order AB-BA is a skew sy...

    Text Solution

    |