Home
Class 12
MATHS
Using properties of determinants in Exer...

Using properties of determinants in Exercises prove that :
`{:[( alpha , alpha ^(2) , beta +gamma ),( beta , beta ^(2) , gamma +alpha ),( gamma , gamma ^(2) ,alpha +beta ) ]:} =(beta -gamma ) (gamma -alpha ) (alpha -beta ) (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 TAMIL|Exercise EXERCISE 4.6|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

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

  • DIFFERENTIAL EQUATIONS

    NCERT TAMIL|Exercise MISCELLANEOUS EXERCISE|18 Videos

Similar Questions

Explore conceptually related problems

Prove that : cos^2 (beta-gamma) + cos^2 (gamma-alpha) + cos^2 (alpha-beta) =1+2cos (beta-gamma) cos (gamma-alpha) cos (alpha-beta) .

If tan^2 alpha tan^2 beta + tan^2 beta tan^2 gamma + tan^2 gamma tan^2 alpha + 2 tan^2 alpha tan^2 beta tan^2 gamma = 1 then sin^2 alpha + sin^2 beta + sin^2 gamma =

If cos alpha + cos beta + cos gamma = sin alpha + sin beta + sin gamma = 0 , show that sin 3alpha + sin 3 beta + sin 3gamma = 3 sin (alpha + beta + gamma)

If cos (alpha - beta) + cos (beta - gamma) + cos (gamma - alpha) = (-3)/(2) then prove that cos alpha + cos beta+ cos gamma = sin alpha + sin beta + sin gamma = 0 .

If alpha , beta , gamma in [0,pi] and if alpha , beta , gamma are in A.P then ( sin alpha - sin gamma)/( cos gamma -cos alpha) is equal to

If cos alpha + cos beta + cos gamma = sin alpha + sin beta + sin gamma = 0 , show that cos 3alpha + cos 3 beta + cos gamma = 3 cos (alpha + beta + gamma) and

If tan beta=2sin alpha sin gamma co sec(alpha+gamma) , then cot alpha,cot beta,cotgamma are in

If A=[(alpha, beta),(gamma, -alpha)] is such that A^(2)=I , then

Prove that |(sin alpha,cos alpha,sin(alpha+delta)),(sin beta,cos beta,sin(beta+delta)),(sin gamma,cos gamma,sin(gamma+delta))|=0

NCERT TAMIL-DETERMINANTS -Miscellaneous Exercises on Chapter 4
  1. Prove that the determinant {:[( x, sin theta ,cos theta ),( -sin thet...

    Text Solution

    |

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

    Text Solution

    |

  3. Evaluate {:[( cos alpha cos beta , cos alpha sin beta , -sin alpha ),...

    Text Solution

    |

  4. If a,b and c are real numbers, and Delta ={:[( b+c,C+a,a+b),( c+a,a...

    Text Solution

    |

  5. Solve the equation {:[( x+a,x,x),(x,x+a,x),(x,x,x+a) ]:}=0,ane 0

    Text Solution

    |

  6. Prove that {:[( a^(2) , bc, ac+c^(2)),( a^(2) +ab,b^(2) ,ac),( ab,b^(2...

    Text Solution

    |

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

    Text Solution

    |

  8. Let A = {:[( 1,2,1),(2,3,1),(1,1,5) ]:} Verify that (A^(-1) )^(-1) =...

    Text Solution

    |

  9. Evaluate {:[( x,y , x+y),( y,x+y,x),( x+y,x,y)]:}

    Text Solution

    |

  10. Evaluate {:[(1,x,y),( 1,x+y,y),( 1,x,x+y)]:}

    Text Solution

    |

  11. Using properties of determinants in Exercises prove that : {:[( alph...

    Text Solution

    |

  12. {:[( x,x^(2) , 1+ px^(3) ),( y,y^(2) , 1+ py^(3)),( z,z^(2) , 1+pz^(3)...

    Text Solution

    |

  13. solve {:[( 3a,-a+b,-a+c),( -b+a, 3b,-b+c) ,( -c+a,-c+b,3c) ]:} = 3( a+...

    Text Solution

    |

  14. {:[( 1,1+p,1+p+q),( 2,3+2p,4+3p+2q),( 3,6+3p,10+6p+3q)]:}=1

    Text Solution

    |

  15. Without expanding evaluate the determinant |(sinalpha,cosalpha,sin(alp...

    Text Solution

    |

  16. Solve system of linear equations , using matrix method 2x+ 3y + ...

    Text Solution

    |

  17. If a,b,c are in A.P. then the determinant {:[( x+2,x+3,x+2a),( x+3,...

    Text Solution

    |

  18. If x,y,z are nonzero real number , then the inverse of matrix A= {:[( ...

    Text Solution

    |

  19. Let A={:[( 1,sin theta , 1),( -sin theta , 1, sin theta ),( -1 ,-sin ...

    Text Solution

    |