Home
Class 12
MATHS
Using peoperties of determinants in ques...

Using peoperties of determinants in questions 11 to 15, prove that :
`|{:(alpha,alpha^(2),beta+gamma),(beta,beta^(2),gamma+alpha),(gamma,gamma^(2),alpha+beta):}|=(beta-gamma)(gamma-alpha)(alpha-beta+gamma)`

Text Solution

Verified by Experts

The correct Answer is:
`x=2,y=3,z=5`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    NCERT GUJARATI|Exercise EXERCISE 4.6|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 5|23 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE|18 Videos

Similar Questions

Explore conceptually related problems

Using properties of determinants in Exercise 11 to 15 prove that |{:(alpha,alpha^2,beta+gamma),(beta,beta^2,gamma+alpha),(gamma,gamma^2,alpha+beta):}|=(beta-gamma)(gamma-alpha)(alpha+beta+gamma)(alpha-beta)

Using properties of determinants in Exercise 11 to 15 prove that |{:(sinalpha,cosalpha,cos(alpha+delta)),(sinbeta,cosbeta,cos(beta+delta)),(singamma,cosgamma,cos(gamma+delta)):}|=0

If alpha, beta, gamma are the roots of the cubic x^(3)-px^(2)+qx-r=0 Find the equations whose roots are (i) beta gamma +1/(alpha), gamma alpha+1/(beta), alpha beta+1/(gamma) (ii) (beta+gamma-alpha),(gamma+alpha-beta),(alpha+beta-gamma) Also find the valueof (beta+gamma-alpha)(gamma+alpha-beta)(alpha+beta-gamma)

The value of |{:(betagamma,betagamma'+beta'gamma,beta'gamma'),(gammaalpha,gammaalpha'+gamma'alpha,gamma'alpha'),(alphabeta,alphabeta'+alpha'beta,alpha'beta'):}| is

Explain alpha beta and gamma rays

if alpha,beta,gamma are the roots of x^3-3x^2 +3x + 7 =0 then (alpha-1)/(beta-1)+(beta-1)/(gamma-1)+(gamma-1)/(alpha-1)

If alpha,beta,gamma are the roots of x^(3)+2x^(2)-x-3=0 The value of |{:(alpha, beta ,gamma),(gamma,alpha ,beta),(beta,gamma ,alpha):}| is equal to

If cos^(-1)alpha+cos^(-1)beta+cos^(-1)gamma=3pi , then alpha(beta+gamma)+beta(gamma+alpha)+gamma(alpha+beta) equals to ______

cos^(2) alpha +cos^(2) beta +cos^(2) gamma is equal to

If a matricx [{:(0,2beta,gamma),(alpha,beta,-gamma),(alpha,-beta,gamma):}] is a orthogonal matrix then ………

NCERT GUJARATI-DETERMINANTS -Miscellaneous Exercises on Chapter 4
  1. Prove that the determinant Delta =|{:(x,,sin0,,cos 0),(-sin 0,,-x,...

    Text Solution

    |

  2. Without expanding the determinant, prove that {:[( a, a ^(2), bc ),( ...

    Text Solution

    |

  3. Evaluate |cosalphacosbetacosalphasinbeta-sinalpha-sinbetacosbeta0sinal...

    Text Solution

    |

  4. If a, b and c are real numbers, and Delta=|b+cc+a a+b c+a a+bb+c a+bb+...

    Text Solution

    |

  5. Solve the equation |x+a xxxx+a xxxx+a|=0, a!= 0

    Text Solution

    |

  6. Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Pr...

    Text Solution

    |

  7. If A-^1=[3-1 1-15 6-5 5-2 2] and B=[1 2-2-1 3 0 0-2 1] , find (A B)^(-...

    Text Solution

    |

  8. Evaluate |[x,y,x+y],[y,x+y,x],[x+y,x,y]|

    Text Solution

    |

  9. Evaluate the following: |[1,x,y],[1, x+y, y],[1, x, x+y]|

    Text Solution

    |

  10. Using peoperties of determinants in questions 11 to 15, prove that : ...

    Text Solution

    |

  11. Using properties of determinants. Prove that |xx^2 1+p x^3y y^2 1+p y^...

    Text Solution

    |

  12. Show that: |(3a,-a+b,-a+c),(-b+a,3b,-b+c),(-c+a,-c+b,3c)|=3(a+b+c)(a b...

    Text Solution

    |

  13. Show that |1 1+p1+p+q2 3+2p1+3p+2q3 6+3p 106 p+3q|=1.

    Text Solution

    |

  14. Without expanding, show that the value of each of the determinants is ...

    Text Solution

    |

  15. Solve the system of equations2/x+3/y+(10)/z=44/x-6/y+5/z=16/x+9/y-(20)...

    Text Solution

    |

  16. Choose the correct answer in questions 17 to 19: If a, b, c are in ...

    Text Solution

    |

  17. Choose the correct answer in questions 17 to 19: If x, y, z are non...

    Text Solution

    |

  18. Let A = [(1,sin theta,1),(- sin theta,1,sin theta),(-1,-sin theta,1)],...

    Text Solution

    |