Home
Class 12
MATHS
If x+y+z=0 prove that | xa yb zc yc ...

If `x+y+z=0` prove that `| xa yb zc yc za xb zb xc ya y|=x y z|a b c c a b b c a|`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA ENGLISH|Exercise All Questions|168 Videos

  • DIFFERENTIABILITY

    RD SHARMA ENGLISH|Exercise All Questions|135 Videos

Similar Questions

Explore conceptually related problems

If x+y+z=0 , prove that |[xa, yb,zc],[yc, za, xb], [zb, xc, ya]|=x y z|[a, b, c],[c ,a, b],[b ,c,c]|

If x+y+z=0 prove that |[a x, b y, c z],[ c y, a z ,b x],[ b z ,c x ,a y]|=x y z|[a, b, c],[c ,a ,b],[b ,c ,a]|

Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=|y b q x a p z c r|

Without expanding, prove that |a b c x y z p q r|=|x y z p q r a b c|=|y b q x a p z c r|

Prove that: |a b a x+b y b c b x+c y a x+b y b x+c y0|=(b^2-a c)(a x^2+2b x y+c y^2) .

Prove that |a x-b y-c z a y+b x c x+a z a y+b x b y-c z-a x b z+c y c x+a z b z+c y c z-a x-b y|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot

If x+y+z=0=a+b+c, then |{:(xa,yb,zc),(yc,za,xb),(zb,xc,ya):}|=

Prove that |[a x-b y-c z, a y+b x, c x+a z], [a y+b x, b y-c z-a x, b z+c y],[c x+a z, b z+c y, c z-a x-b y]|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot

Show that |a b c a+2x b+2y c+2z x y z|=0

Show 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|

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-...

    Text Solution

    |

  2. If a , b , c are all positive and are p t h ,q th and r t h terms of a...

    Text Solution

    |

  3. If x+y+z=0 prove that | xa yb zc yc za xb zb xc ya y|=x y z|a b c...

    Text Solution

    |

  4. Prove that: |[b, c-a^2,c] ,[a-b^2,a b-c^2,c ],[a-b^2,a ,b-c^2b c-a^2a ...

    Text Solution

    |

  5. Prove that: |[bc-a^2, ca-b^2,ab-c^2],[ca-b^2,ab-c^2,bc-a^2],[ab-c^2,bc...

    Text Solution

    |

  6. Find a quadratic polynomial varphi(x) whose zeros are the maximum ...

    Text Solution

    |

  7. f(x)=|(secx,cos x,sec^2x + cot x cosecx),(cos^2x,cos^2x,cosec^2 x),(1,...

    Text Solution

    |

  8. Let "T"r=|[r ,x,(n(n+1))/2], [2r-1,y, n^2],[ 3r-2,z,(n(3n-1))/2]| .whe...

    Text Solution

    |

  9. If "Delta"r=|[2^(r-1),2. 3^(r-1),4. 5^(r-1)],[x, y ,z],[2^n-1, 3^n-1, ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. Without expanding,FIND "Delta"=|(((a-x)^2),((a-y)^2),((a-z)^2)),(((b-x...

    Text Solution

    |

  13. Prove that: |(-2a , a+b, a+c),( b+a,-2b, b+c),( c+a , c+b,-2c)|=4(a+b...

    Text Solution

    |

  14. Evaluate the following determinant: |[1 ,3, 5], [2 ,6, 10], [31, 11,...

    Text Solution

    |

  15. Evaluate the following determinant: |[1, 4, 9], [4 ,9 ,16], [9, 16, ...

    Text Solution

    |

  16. Without expanding, show that the value of each of the following dete...

    Text Solution

    |

  17. Without expanding, show that the value of each of the following dete...

    Text Solution

    |

  18. Without expanding, show that the value of the following determinant ...

    Text Solution

    |

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

    Text Solution

    |

  20. Without expanding, show that the value of the following determinant...

    Text Solution

    |