Home
Class 12
MATHS
Without expanding evaluate the determi...

Without expanding evaluate the determinant `"Delta"=|(1, 1, 1),(a, b, c),( a^2,b^2,c^2)|` .

Text Solution

Verified by Experts

The correct Answer is:
k=1
`Delta= [[1 ,a ,a^{2}] , [1 ,b ,b^{2} ], [1 ,c ,c^{2}]]`
`R_1 rightarrow R_1 -R_3`
`R_2 rightarrow R_2 -R_3`
`[[0 , a-b , a^{2}-b^{2} ], ...
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

  • DIFFERENTIABILITY

    RD SHARMA|Exercise Solved Examples And Exercises|136 Videos

Similar Questions

Explore conceptually related problems

without expanding evaluate the determinant Delta=det[[1,1,1a,b,ca^(2),b^(2),c^(2)]]

Without expanding the determinant , prove that |{:(a, a^(2),bc),(b,b^(2),ca),(c,c^(2),ab):}|=|{:(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3)):}|

Without expanding, prove that each of the following determinant vanishes : |(1,a,b+c),(1,b,c+a),(1,c,a+b)|

The value of the determinant |{:(1,a, a^(2)-bc),(1, b, b^(2)-ca),(1, c, c^(2)-ab):}| is…..

Without expanding, show that the value of each of the determinants is zero: |[1,a, a^2-bc],[1,b,b^2-ac],[1,c,c^2-ab]|

Without expanding, show that the value of each of the determinants is zero: |1/a a^2b c a/bb^2a c a/cc^2a b|

Without expanding the determinant,prove ,a,a^(2),bcb,b^(2),cac,c^(2),ab]|=det[[1,a^(2),a^(3)1,b^(2),b^(3)1,c^(2),c^(3)]]

Without expanding the determinant prove that abs([a,a^2,bc],[b,b^2,ca],[c,c^2,ab])=abs([1,a^2,a^3],[1,b^2,b^3],[1,c^2,c^3])

Without expanding, prove that the following determinants vanish : |{:(a,b,a+b),(b,c,b+c),(c,a,c+a):}|

If a,b,c are unequal then what is the condition that the value of the following determinant is zero Delta =|(a,a^2,a^3+1),(b,b^2,b^3+1),(c,c^2,c^3+1)|

RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. If "Delta"r=|2^(r-1)2. 3^(r-1)4. 5^(r-1)x y z2^n-1 3^n-1 5^n-1|dot Sho...

    Text Solution

    |

  2. If m is a positive integer and Dr=|(2r-1,\ ^m Cr,1),(m^2-1, 2^m ,m+1...

    Text Solution

    |

  3. Without expanding evaluate the determinant "Delta"=|(1, 1, 1),(a, b,...

    Text Solution

    |

  4. Without expanding, show that "Delta"=|(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y...

    Text Solution

    |

  5. Prove that: |-2a a+b a+c b+a-2bb+cc+a c+b-2c|=4(a+b)(b+c)(c+a)

    Text Solution

    |

  6. Without expanding, show that the value of each of the following det...

    Text Solution

    |

  7. Prove: |(1,b+c ,b^2+c^2),( 1,c+a ,c^2+a^2),( 1,a+b ,a^2+b^2)|=(a-b)(b-...

    Text Solution

    |

  8. Prove: |(a, a+b, a+2b),( a+2b, a ,a+b ),(a+b, a+2b, a)|=9(a+b)b^2

    Text Solution

    |

  9. Prove: |(1,a, b c),(1,b ,c a),(1,c ,a b)|=|(1,a ,a^2),( 1,b,b^2),( 1,c...

    Text Solution

    |

  10. Prove: |(a^2,b c, a c+c^2),(a^2+a b,b^2,a c ),(a b,b^2+b c,c^2)|=4a^2b...

    Text Solution

    |

  11. Prove: |(x+4,x,x),(x,x+4,x),(x,x,x+4)|=16(3x+4)

    Text Solution

    |

  12. Show that |[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|=

    Text Solution

    |

  13. Prove: |(a, b-c,c-b),( a-c, b, c-a),( a-b,b-a, c)|=(a+b-c)(b+c-a)(c+a-...

    Text Solution

    |

  14. Prove: |a^2+1a b a c a bb^2+1b cc a c b c^2+1|=1+a^2+b^2+c^2

    Text Solution

    |

  15. Prove: |1a a^2a^2 1a a a^2 1|=(a^3-1)^2

    Text Solution

    |

  16. Prove: |b+c a a b c+a b cc a+b|=4a b c

    Text Solution

    |

  17. Show that |[b^2+c^2,ab,ac],[ba,c^2+a^2,bc],[ca,cb,a^2+b^2]|=4a^2b^2c^2

    Text Solution

    |

  18. Prove: |(0,b^2a, c^2a),( a^2b,0,c^2b),( a^2c, b^2c,0)|=2a^3b^3c^3

    Text Solution

    |

  19. Prove: |((a^2+b^2)/c,c,c),( a,(b^2+c^2)/a ,a),( b,b,(c^2+a^2)/b)|=4a b...

    Text Solution

    |

  20. Prove: |(-bc, b^2+b c,c^2+bc), (a^2+a c,-a c,c^2+a c),( a^2+a b,b^2+a ...

    Text Solution

    |