Home
Class 12
MATHS
Prove that: (i) |{:(,1,1,1),(,a,b,c),(,...

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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • MATRICES & DETERMINANT

    RESONANCE ENGLISH|Exercise SECTION-C|10 Videos

  • MATRICES & DETERMINANT

    RESONANCE ENGLISH|Exercise SECTION-D|17 Videos

  • MATRICES & DETERMINANT

    RESONANCE ENGLISH|Exercise EXERCISE-1|9 Videos

  • INDEFINITE INTEGRATION

    RESONANCE ENGLISH|Exercise SELF PRACTIC PROBLEMS|25 Videos

  • NUMBER THEORY

    RESONANCE ENGLISH|Exercise Exercise -2 (PART - II)|4 Videos

Similar Questions

Explore conceptually related problems

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

Prove that : |{:(a+b,b+c,c+a),(c,a,b),(1,1,1):}|

Prove that : |{:(a+b,b,c),(b+c,c,a),(c+a,a,b):}|=3 abc-a^(3)-b^(3)-c^(3)

By using properties of determinants. Show that: (i) |[1,a, a^2],[ 1,b,b^2],[ 1,c,c^2]|=(a-b)(b-c)(c-a) (ii) |[1, 1, 1],[a, b, c],[ a^3,b^3,c^3]|=(a-b)(b-c)(c-a)(a+b+c)

Prove that (a+b+c)^(3)-a^(3)-b^(3)-c^(3)=3(a+b)(b+c)(c+a) .

Show that |[a ,b ,c],[ a^2,b^2,c^2],[bc, ca, ab]|=|[1, 1, 1],[a^2,b^2,c^2],[a^3,b^3,c^3]|=(a-b)(b-c)(c-a)(a b+b c+c a) .

Prove: |a^3 2a b^3 2b c^3 2c|=2(a-b)(b-c)(c-a(a+b+c)

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

" if " |{:(1,,1,,1),(a,,b,,c),(bc,,ca,,ab):}|=|{:(1,,1,,1),(a,,b,,c),(a^(3),,b^(3),,c^(3)):}| where a,b,c are distinct positive reals then the possible values of abc is // are

If A=|(1,1,1),(a,b,c),(a^3,b^3,c^3)|, B=|(1,1,1),(a^2,b^2,c^2),(a^3,b^3,c^3)|, C=|(a,b,c),(a^2,b^2,c^2),(a^3,b^3,c^3)| , then which relation is correct :

RESONANCE ENGLISH-MATRICES & DETERMINANT-SECTION-B
  1. If minor of three-one element (i.e.M(31)) in the determinant [{:(,0,1,...

    Text Solution

    |

  2. Using the properties of detminants, evalulate. (i) |{:(,23,6,11),(,36...

    Text Solution

    |

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

    Text Solution

    |

  4. about to only mathematics

    Text Solution

    |

  5. Find the non-zero roots of the equation. (i) Delta=|{:(,a,b,ax+b),(,...

    Text Solution

    |

  6. If Sr = alpha^r + beta^r + gamma^r then show that |[S0,S1,S2],[S1,S2,S...

    Text Solution

    |

  7. The value of |(a(1) x(1) + b(1) y(1),a(1) x(2) + b(1) y(2),a(1) x(3) +...

    Text Solution

    |

  8. If [{:(,e^(x),sin x),(,cos x,ln(1+x))]:}=A+Bx+Cx^(2)+....... then find...

    Text Solution

    |

  9. If A and B are squar matrices of order 3 such that |A|=-1, |B|=3 then ...

    Text Solution

    |

  10. Let A=[(cos^(- 1)x,cos^(- 1)y,cos^(- 1)z),(cos^(- 1)y,cos^(- 1)z,cos^...

    Text Solution

    |

  11. Find the value of the determinant |{:(-1,2,1),(3+2sqrt(2),2+2sqrt(2)...

    Text Solution

    |

  12. If alpha,beta,gamma are roots of the equation x^(3)+px+q=0 then the va...

    Text Solution

    |

  13. If a, b,c> 0 and x,y,z in RR then the determinant |((a^x+a^-x)^2,(a...

    Text Solution

    |

  14. If a,b and c are non- zero real number then prove that |{:(b^(2...

    Text Solution

    |

  15. The determinant |(b(1)+c(1),c(1)+a(1),a(1)+b(1)),(b(2)+c(2),c(2)+a(2...

    Text Solution

    |

  16. If x,y,z in R & Delta =|(x,x+y,x+y+z),(2x,5x+2y,7x+5y+2z),(3x,7x+3y,9x...

    Text Solution

    |

  17. if determinant |{:( cos (0 + phi),,-sin (0+phi),,cos 2phi),(sin 0,,cos...

    Text Solution

    |

  18. about to only mathematics

    Text Solution

    |