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

Without expanding evaluate the determinant `|(x^2+x^(-1))^2(a^2-a^(-1))^2 1(a^y+a^(-y))^2(a^y-a^(-y))^2 1(a^2+a^(-z))^2(a^z-a^(-z))^2 1|,` where `a , >0a n dx , y , z in Rdot`

Text Solution

Verified by Experts

145829
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

The value of Delta = |((a^(x) + a^(-x))^(2),(a^(x) -a^(-x))^(2),1),((a^(y) + a^(-y))^(2),(a^(y) -a^(-y))^(2),1),((a^(z) + a^(-z))^(2),(a^(z) - a^(-z))^(2),1)| , is

If a, b,c> 0 and x,y,z in R then the determinant: |((a^x+a^-x)^2,(a^x-a^-x)^2,1),((b^y+b^-y)^2,(b^y-b^-y)^2,1),((c^z+c^-z)^2,(c^z-c^-z)^2,1)| is equal to

The value of the determinant |{:(1,x,x^2),(1,y,y^2),(1,z,z^2):}| is equal to

The value of the determinant |{:(x^(2),1,y^(2)+z^(2)),(y^(2),1,z^(2)+x^(2)),(z^(2),1,x^(2)+y^(2)):}| is :

Show that: ((a^(x+1))/(a^(y+1)))^(x+y)((a^(y+2))/(a^(z+2)))^(y+z)((a^(z+3))/(a^(x+3)))^(z+x)=1

If x,y,z are distinct real numbers then the value of ((1)/(x-y))^(2)+((1)/(y-z))^(2)+((1)/(z-x))^(2) is

(1)/((x-y)^(2))+(1)/((y-z)^(2))+(1)/((z-x)^(2))=((1)/(x-y)+(1)/(y-z)+(1)/(z-x))^(2)

If x+y+z=0 then what is the value of (1)/(x^(2)+y^(2)-z^(2)) +(1)/(y^(2)+z^(2)-x^(2)) +(1)/(z^(2)+x^(2)-y^(2)) ?

If |(x,x^(2),1+x^(2)),(y,y^(2),1+y^(2)),(z,z^(2),1+z^(2))| where x, y, z are distinct what is |A| ?

RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. Without expanding show that |b^2c^2b c b+cc^2a^2c a c+a a^2b^2a b a...

    Text Solution

    |

  2. Without expanding evaluate the determinant |sinalphacosalphasin(alp...

    Text Solution

    |

  3. Without expanding evaluate the determinant |(x^2+x^(-1))^2(a^2-a^(-1))...

    Text Solution

    |

  4. If a ,\ b ,\ c are in A.P., find the value of |2y+4 5y+7 8y+a3y+5 6...

    Text Solution

    |

  5. Without expanding evaluate the determinant =|265 240 219 240 225 19...

    Text Solution

    |

  6. If 1=|1 1 1x^2y^2z^2x y z| and 2=|1 1 1y z z xx y x y z| , without exp...

    Text Solution

    |

  7. Let =|A xx^2 1B y y^2 1C z z^2 1| and 1=|A B C x y z y z z xx y| , the...

    Text Solution

    |

  8. If 1=|a b c x y z p q r| and 2=|q-b y-p a-x r-c z| , without expanding...

    Text Solution

    |

  9. If A is a skew-symmetric matrix of odd order n , then |A|=O .

    Text Solution

    |

  10. Prove that: |0a-b-a0-c b c0|=0 .

    Text Solution

    |

  11. Without expanding or evaluating show that |0b-a c-a a-b0c-b a-c b-c...

    Text Solution

    |

  12. Without expanding, prove that |a+b x c+dx p+q x a x+b c x+d p x+q u...

    Text Solution

    |

  13. Prove that: |-a^2a b a c b a-b^2b c a c b c-c^2|=4a^2b^2c^2 .

    Text Solution

    |

  14. Prove that: |1 1 1 1 1+x1 1 1 1+y|=x y .

    Text Solution

    |

  15. Evaluate: |1a a^2 1bb^2 1cc^2| .

    Text Solution

    |

  16. Show that : |x y z x^2y^2z^2x^3y^3z^3|=x y z(x-y)(y-z)(z-x)dot

    Text Solution

    |

  17. Prove that: |alphabetagammaalpha^2beta^2gamma^2beta+gammagamma+alphaal...

    Text Solution

    |

  18. In a triangleABC, if |[1,1,1][1+sinA,1+sinB,1+sinC],[sinA+sin^2A,sinB+...

    Text Solution

    |

  19. In a A B C ,if|1 1 1 1+cosA1+cosB1+cosCcos^2A+cosBcos^2A+cosBcos^2+co...

    Text Solution

    |

  20. Show that |[a ,b ,c],[ a^2,b^2,c^2],[bc, ca, ab]|=|[1, 1, 1],[a^2,b^2,...

    Text Solution

    |