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

Using properties of determinants, prove that `|a+x y z x a+y z x y a+z|=a^2(a+x+y+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 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 .

Using Properties of determinants, prove that: {:|(x^2+1,xy,yz),(xy,y^2+1,yz),(xz,yz,z^2+1)|=1+x^2+y^2+z^2

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 {:|( x,a,x+a),( y,b,y+b),(z,c,z+c)|:} =0

Find the product of (5x - y +z) (5x - 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)|:}

The value of the determinant |{:(1 , x , x+ z) , (1 , y , z + x) , (1 , z , x + y):}| is

(a)Find x+y+z

Solve the following system of linear equations by matrix method : 3x - 2y + 3z = 8, 2x + y - z = 1, 4x - 3y + 2z = 4

Prove that |[x+y+2z,x,y],[z,y+z+2x,y],[z,x,z+x+2y]|= 2(x+y+z)^(3)

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

    Text Solution

    |

  2. |[b+c, a,a] , [b,c+a,b] , [c,c,a+b]|=4abc

    Text Solution

    |

  3. Using properties of determinants, prove that |a+x y z x a+y z x y a+z...

    Text Solution

    |

  4. Using Properties of determinants, prove that {:|(x+lamda,2x,2x),(2...

    Text Solution

    |

  5. Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Pr...

    Text Solution

    |

  6. Prove: |2y y-z-x2y2z2z z-x-y x-y-z2x2x|=(x+y+z)^3

    Text Solution

    |

  7. Using Properties of determinants, prove that: {:|(x^2+1,xy,yz),(xy,y...

    Text Solution

    |

  8. Prove that: |(a^2+1, ab, ac),(ab, b^2+1, bc),(ac, bc, c^2+1)|=1+a^2+b^...

    Text Solution

    |

  9. Using Properties of determinants, prove that {:|(x+y,x,x),(5x+4y,4x,...

    Text Solution

    |

  10. Using Properties of determinants, prove that: {:|(b+c,c+a,a+b),(q+r,...

    Text Solution

    |

  11. IF a+b+c ne 0 and {:|(a,b,c),(b,c,a),(c,a,b)|=0, then using properties...

    Text Solution

    |

  12. Prove that |[1,a,a^3],[1,b,b^3],[1,c,c^3]|=(a-b)(b-c)(a+b+c)

    Text Solution

    |

  13. Prove that: (i) |{:(,1,1,1),(,a,b,c),(,a^(3),b^(3),c^(3)):}|=(a-b)(b...

    Text Solution

    |

  14. Prove that : |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|=(a-b)(b-c)(c...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |