Home
Class 12
MATHS
The value of the determinant (a1-b1)^2(...

The value of the determinant `(a_1-b_1)^2(a_1- b_2)^2(a_1-b_3)^2(a_1-b_4)^2(a_2-b_1)^2(a_2-b_2)^2(a_2-b_3)^2(a_2- b_4)^2(a_3-b_1)^2(a_3-b_2)^2(a_3-b_3)^2(a_3-b_4)^2(a_4-b_1)^2(a_4-b_2)^2(a_4-b_3)^2(a_4-b_4)^2` is dependant on `a_i , i=1,2,3,4` dependant on `b_i , i=1,2,3,4` dependant on `a_(i j), b_i i=1,2,3,4`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

Similar Questions

Explore conceptually related problems

If (b_2-b_1)(b_3-b_1)+(a_2-a_1)(a_3-a_1)=0 , then prove that the circumcenter of the triangle having vertices (a_1,b_1),(a_2,b_2) and (a_3,b_3) is ((a_(2+a_3))/2,(b_(2+)b_3)/2)

If a_1, a_2, ,a_n >0, then prove that (a_1)/(a_2)+(a_2)/(a_3)+(a_3)/(a_4)++(a_(n-1))/(a_n)+(a_n)/(a_1)> n

If f(x)=(a_1x+b_1)^2+(a_2x+b_2)^2+...+(a_n x+b_n)^2 , then prove that (a_1b_1+a_2b_2++a_n b_n)^2lt=(a1 2+a2 2++a n2)^(b1 2+b2 2++b n2)dot

If x = a cos θ and y = b sin θ, then b2x2 + a2y2 = …………… (1) a2b2 (2) ab (3) a4b4 (4) a2 + b2

If a_1,a_2, a_3, a_4 be the coefficient of four consecutive terms in the expansion of (1+x)^n , then prove that: (a_1)/(a_1+a_2)+(a_3)/(a_3+a_4)=(2a_2)/(a_2+a_3)dot

If a_1,a_2,a_3….a_(2n+1) are in A.P then (a_(2n+1)-a_1)/(a_(2n+1)+a_1)+(a_2n-a_2)/(a_(2n)+a_2)+....+(a_(n+2)-a_n)/(a_(n+2)+a_n) is equal to

If (1+x)^5=a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5, then the value of (a_0-a_2+a_4)^2+(a_1-a_3+a_5)^2 is equal to 243 b. 32 c. 1 d. 2^(10)

If a_1,a_2,….a_n are in H.P then (a_1)/(a_2+,a_3,…,a_n),(a_2)/(a_1+a_3+….+a_n),…,(a_n)/(a_1+a_2+….+a_(n-1)) are in

Prove that the value of each the following determinants is zero: |[a_1,l a_1+mb_1,b_1],[a_2,l a_2+mb_2,b_2],[a_3,l a_3+m b_3,b_3]|

If Delta=|(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)| and Delta_1=|(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 Delta_1=

CENGAGE-DETERMINANTS-All Questions
  1. If (x)=|alpha+xtheta+xlambda+xbeta+xvarphi+xmu+xgamma+xpsi+x v+x| show...

    Text Solution

    |

  2. The value of determinant |b c-a^2a c-b^2a b-c^2a c-b^2a b-c^2b c-a^2a ...

    Text Solution

    |

  3. The value of the determinant (a1-b1)^2(a1- ...

    Text Solution

    |

  4. If l1^2+m1^2+n1^2=1 etc., and l1 l2+m1 m2+n1 n2 = 0, etc. and Delta...

    Text Solution

    |

  5. Integrate (sinx)/((sinx-cosx))dx=?

    Text Solution

    |

  6. The value of determinant |[ ^n C(r-1), ^n Cr, (r+1)^(n+2)C(r+1)],[ ^n...

    Text Solution

    |

  7. Let |{:(x,,2,,x),(x^(2),,x,,6),(x,,x,,6):}|=Ax^(4) +Bx^(3)+Cx^(2)+Dx+E...

    Text Solution

    |

  8. Let a ,b , c be the real numbers. The following system of equations in...

    Text Solution

    |

  9. The value of the determinant |[sintheta, costheta, sin2theta] , [sin(t...

    Text Solution

    |

  10. Find the value of the determinant |b cc a a b p q r1 1 1|,w h e r ea ,...

    Text Solution

    |

  11. let a > 0 , d > 0 find the value of the determinant |[1/a,1/(a(a + d))...

    Text Solution

    |

  12. For all values of A,B,C and P,Q,R show that |{:(cos(A-P),,cos(A-Q)...

    Text Solution

    |

  13. Let lambdaa n dalpha be real. Find the set of all values of lambda for...

    Text Solution

    |

  14. Prove that |a x-b y-c z a y+b x c x+a z a y+b x b y-c z-a x b z+c y c...

    Text Solution

    |

  15. If (x)=|alpha+xtheta+xlambda+xbeta+xvarphi+xmu+xgamma+xpsi+x v+x| show...

    Text Solution

    |

  16. If alpha,beta,gamma are different from 1 and are the roots of a x^3+b ...

    Text Solution

    |

  17. If p+q+r=0=a+b+c =0, then the value of the determnalnt |p a q b r c q ...

    Text Solution

    |

  18. Let =|2a1b1a1b2+a2b1a1b3+a3b1a1b2+a2b1 2a2b2a2b3+a3b2a1b3+a3b1a3b2+a2b...

    Text Solution

    |

  19. If 2s=a+b+c and A=|[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[(s-c)^...

    Text Solution

    |

  20. Evaluate |^x C1^x C2^x C3^y C1^y C2^y C3^z C1^z C2^z C3|

    Text Solution

    |