Home
Class 12
MATHS
Using the property of determinants and w...

Using the property of determinants and without expanding prove the following
`|{:(a,b,c),(a+2x,b+2y,c+2z),(x,y,z):}|=0`

Text Solution

Verified by Experts

The correct Answer is:
0
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Short Answer Type Questions)|17 Videos

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Long Answer Type Questions)|6 Videos

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Textbook based MCQs|42 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    KUMAR PRAKASHAN|Exercise Practice Paper - 5 (Section-D)|4 Videos

  • INTEGRALS

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER-7 (SECTION-D)|2 Videos

Similar Questions

Explore conceptually related problems

Using the property of determinants and without expanding prove the following |{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|=0

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,1,1),(a,b,c),(a^3,b^3,c^3):}|=(a-b)(b-c)(c-a)(a+b+c)

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(0,a,-b),(-a,0,-c),(b,c,0):}|=0

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b):}|=(a+b+c)^3

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(1,bc,a(b+c)),(1,ca,b(c+a)),(1,ab,c(a+b)):}|=0

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1):}|=1+a^2+b^2+c^2

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(x+y+2z,x,y),(z,y+z+2x,y),(z,x,z+x+2y):}|=2(x+y+z)^3

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c):}|=0

Using the property of determinants andd without expanding in following exercises 1 to 7 prove that |{:(-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2):}|=4a^2b^2c^2

KUMAR PRAKASHAN-DETERMINANTS -Textbook Illustrations for Practice work
  1. Evaluate Delta =|{:(3,2,3),(2,2,3),(3,2,3):}|

    Text Solution

    |

  2. Evaluate {:[( 102,18,36),( 1,3,4),( 17,3,6)]:}

    Text Solution

    |

  3. Using the property of determinants and without expanding prove the fol...

    Text Solution

    |

  4. Prove that |{:(a,a+b,a=b+c),(2a,3a+2b,4a+3b+2c),(3a,6a+3b,10a+6b+3c):}...

    Text Solution

    |

  5. Without expanding prove that Delta=|{:(x+y,y+z,z+x),(z,x,y),(1,1,1):...

    Text Solution

    |

  6. Evaluate Delta=|{:(1,a,bc),(1,b,ca),(1,c,ab):}|

    Text Solution

    |

  7. Prove that {:[( b+c,a,a), ( b,c+a,b),( c,c,b+a) ]:}

    Text Solution

    |

  8. If x,y,z are different and Delta=|{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z...

    Text Solution

    |

  9. Prove that |{:(a+1,1,1),(1,b+1,1),(1,1,c+1):}|=abc(1/a+1/b+1/c+1)

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. Find the minor of elements 6 in the determinant Delta=|{:(1,2,3),(4,...

    Text Solution

    |

  13. Find minors and cofactors of all the elements of the determinant |{:(1...

    Text Solution

    |

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

    Text Solution

    |

  15. Find minors and cofactors of the elements of the determinant |{:(2,-3,...

    Text Solution

    |

  16. Find adj A for A = {:[( 2,3),( 1,4) ]:}

    Text Solution

    |

  17. If A=[{:(1,3,3),(1,4,3),(1,3,4):}] , then verify that A adjA=|A|I. Als...

    Text Solution

    |

  18. If A=[{:(2,3),(1,-4):}] and B=[{:(1,-2),(-1,3):}] then verify that (AB...

    Text Solution

    |

  19. Show that the matrix A=[{:(2,3),(1,2):}] satisfies the equation A^2-4A...

    Text Solution

    |

  20. Solve the system of equations {:(2x+5y=1),(3x+2y=7):},

    Text Solution

    |