Home
Class 12
MATHS
Using properties of determinants, pro...

Using properties of determinants, prove that `|b+c q+r y+z c+a r+p z+x c+b p+q x+y|=2\ |a p x b q y c r z|`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    OSWAAL PUBLICATION|Exercise TOPIC -1 DETERMINANTS, MINORS & COFACTORS (LONG ANSWER TYPE QUESTION -II)|3 Videos
  • DETERMINANTS

    OSWAAL PUBLICATION|Exercise TOPIC-2 SOLUTIONS OF SYSTEM OF LINEAR EQUATIONS (LONG ANSWER TYPE QUESTIONS -II )|24 Videos
  • DETERMINANTS

    OSWAAL PUBLICATION|Exercise TOPIC -1 DETERMINANTS, MINORS & COFACTORS (SHORT ANSWER TYPE QUESTIONS-II)|6 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    OSWAAL PUBLICATION|Exercise MVT AND ROLLE.S THEOREM ( SHORT ANSWER TYPE QUESTIONS-II)|5 Videos
  • DIFFERENTIAL EQUATIONS

    OSWAAL PUBLICATION|Exercise HOMOGENEOUS DIFFERENTIAL EQUATIONS (Long Answer Type Questions - III)|8 Videos

Similar Questions

Explore conceptually related problems

Using Properties of determinants, prove that: {:|(b+c,c+a,a+b),(q+r,r+p,p+q),(y+z,z+x,x+y)|=2{:|(a,b,c),(p,q,r),(x,y,z)|

Using the property of determinants and without expanding {:|( b+c,q+r,y+z),( c+a,r+p,z+x),( a+b,p+q,x+y) |:}=2 {:|(a,p,x),( b,q,y),(c,r,z)|:}

using properties of determinant prove that {:[( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(2)),( z,z^(2) , 1+pz^(2)) ]:} =( 1+pxyz ) ( x-y) ( y-z ) (z-x) , where p is any scalar .

|(b+c, q+r, y+z),(c+a,r+p,z +x),(a+b,p+q,x+y)|=2|(a,p,x),(b,q,y),(c,r,z)|

Using the property of determinants and without expanding {:|( x,a,x+a),( y,b,y+b),(z,c,z+c)|:} =0

If a, b, c are in G.P then the value of the determinant Delta= [[a, b, ax+by],[b ,c ,b x+c y],[a x+b y, b x+c y, 0]] is

The roots of the equation (q- r) x^(2) + (r - p) x + (p - q)= 0 are

Sum of X + Y + Z + P =

If (x+i y)^5=p+i q , then prove that (y+i x)^5=q+i pdot

Prove that |(x,p,q),(p,x,q),(p,q,x)| = (x - p)(x - q)(x + p +q)

OSWAAL PUBLICATION-DETERMINANTS-TOPIC -1 DETERMINANTS, MINORS & COFACTORS (LONG ANSWER TYPE QUESTIONS-I)
  1. Prove that : |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|=(a-b)(b-c)(c...

    Text Solution

    |

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

    Text Solution

    |

  3. Using properties of determinants, prove the following: |xx+y x+2y\...

    Text Solution

    |

  4. Using properties of determinants, prove the following: |alphabetag...

    Text Solution

    |

  5. 15. Using properties of determinants, prove the following |[a,b,c],[a-...

    Text Solution

    |

  6. [[b+c,a-b,a],[c+a,b-c,b],[a+b,c-a,c]] = 3abc - a^3 - b^3 - c^3

    Text Solution

    |

  7. Prove that |[a^2, a^2-(b-c)^2, bc],[b^2, b^2-(c-a)^2, ca],[c^2, c^2-(...

    Text Solution

    |

  8. Prove that |(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,c)|=(a+b+c)(a^(2)+b^(2)...

    Text Solution

    |

  9. Using properties of determinants, prove that |b+c q+r y+z c+a r+p ...

    Text Solution

    |

  10. Using the Properties of determinants, prove that following: {:|(-a^2...

    Text Solution

    |

  11. Using the Properties of determinants, prove the following: {:|(1,1...

    Text Solution

    |

  12. If |{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z, z^2,1+z^3):}|=0 and x, y, z are ...

    Text Solution

    |

  13. Using properties of determinants, solve the following for x: |x-2 ...

    Text Solution

    |

  14. Using properties of determinants, solve for x:|a+x a-x a-x a-x a+x a...

    Text Solution

    |

  15. Using Properties of determinants, solve the following for x: {:|(x+a...

    Text Solution

    |

  16. Prove, using properties of determinants: |y+k y y y y+k y y y y+k|=k^...

    Text Solution

    |

  17. Prove |[-bc, b^2+bc, c^2+bc] , [a^2+ac, -ac, c^2+ac] , [a^2+ab, b^2+ab...

    Text Solution

    |

  18. Prove that: |(b+c)^2a^2a^2b^2(c+a)^2b^2c^2c^2(a+b)^2|=2a b c(a+b+c)^2

    Text Solution

    |

  19. |(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a)|=2(3abc-a^(3)-b^(3)-c^(3))

    Text Solution

    |

  20. Prove, using Properites of determinants, {:|(a+bx^2,c+dx^2,p+qx^2),(...

    Text Solution

    |