Home
Class 11
MATHS
Without expanding the determinant, prove...

Without expanding the determinant, prove that:
`|{:(alpha xi, beta psi, gamma zeta),(xi^(2), psi^(2), zeta^(2)),(1,1,1):}| =|{:(alpha, beta, gamma),(xi,psi, zeta),(psi zeta,zeta xi, psi zeta):}|`

Promotional Banner

Topper's Solved these Questions

  • MATRICES

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISES (EXERCISE -3( e)|15 Videos

  • MATRICES

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISES (EXERCISE -3( f)|12 Videos

  • MATRICES

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISES (EXERCISE -3( c)|10 Videos

  • MATHEMATICAL INDUCTION

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Exercise 2 (a)|15 Videos

  • PAIR OF STRAIGHT LINES

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE - 4(c) III. |3 Videos

Similar Questions

Explore conceptually related problems

Without expanding the determinant, prove that: (i) |{:(alpha, alpha^(2), beta gamma),(beta, beta^(2), gamma alpha),(gamma, gamma^(2), alpha beta):}| =|{:(1,alpha^(2), alpha^(3)),(1, beta^(2), beta^(3)),(1, gamma^(2), gamma^(3)):}|

Without expanding the determinant, prove that: |{:(1, beta gamma, beta + gamma),(1, gamma alpha, gamma + alpha),(1, alpha beta, alpha + beta):}| = |{:(1, alpha, alpha^(2)),(1, beta, beta^(2)),(1, gamma, gamma^(2)):}|

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

If alpha+beta=gamma. then cos^(2)alpha+cos^(2)beta+cos^(2)gamma-2 cos alpha cos beta cos gamma=

If alpha, beta, gamma are the roots of x^(3) + x^(2) + x + 1 = 0 then alpha^(2) + beta^(2) + gamma^(2) =

sin 2 alpha + sin 2 beta + sin 2 gamma - sin2(alpha + beta + gamma )=

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

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-MATRICES -TEXTUAL EXERCISES (EXERCISE -3( d)
  1. |(a,b,c),(b,c,a),(c,a,b)|=

    Text Solution

    |

  2. Find the determinant of the matrix [(1^(2),2^(2),3^(2)),(2^(2),3^(2),4...

    Text Solution

    |

  3. IF A=[{:(1,0,0),(2,3,4),(5,-6,x):}] and det A=45 then find x.

    Text Solution

    |

  4. Show that |{:(bc,b+c,1),(ca,c+a,1),(ab,a+b,1):}|=(a-b)(b-c)(c-a)

    Text Solution

    |

  5. |(b+c, c+a, a+b),(a+b, b+c, c+a),(a, b,c)]=a^(3)+b^(3)+c^(3)-3abcఅని చ...

    Text Solution

    |

  6. Prove that |{:(y+z,x,x),(y,z+x,y),(z,z,x+y):}|=4xyz

    Text Solution

    |

  7. |(a, a^(2),1+a^(3)),(b,b^(2),1+b^(3)),(c,c^(2),1+c^(3))|=0, |(a, a^(2)...

    Text Solution

    |

  8. Without expanding the determinant, prove that: (i) |{:(alpha, alpha^...

    Text Solution

    |

  9. Without expanding the determinant, prove that: |{:(alpha xi, beta psi...

    Text Solution

    |

  10. Without expanding the determinant, prove that: |{:(1, beta gamma, be...

    Text Solution

    |

  11. If Delta(1)=|{:(a(1)^(2)+b(1)+c(1),a(1)a(2)|b(2)|c(2),a(1)a(3)+b(3)+c(...

    Text Solution

    |

  12. Delta1=|(1,cos alpha, cos beta),(cos alpha , 1, cos gamma),(cos beta, ...

    Text Solution

    |

  13. Show that |{:(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b):}|=2(a+b+c)^3

    Text Solution

    |

  14. Show that |{:(a,b,c),(b,c,a),(c,a,b):}|^2=|{:(2bc-a^(2),c^(2),b^(2)),(...

    Text Solution

    |

  15. Show that |{:(a^2+2a,2a+1,1),(2a+1,a+2,1),(3,3,1):}|=(a-1)^3

    Text Solution

    |

  16. Show that |{:(a,b,c),(a^(2),b^(2),c^(2)),(a^(2),b^(3),c^(3)):}|=abc(a-...

    Text Solution

    |

  17. Show that A=|{:(-2a,a+b,c+a),(a+b,-2b,b+c),(c+a,c+b,-2c):}|=4(a+b)(b+c...

    Text Solution

    |

  18. Show that |{:(a-b,b-c,c-a),(b-c,c-a,a-b),(c-a,a-b,b-c):}|=0

    Text Solution

    |

  19. Show that |{:(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab):}|=0

    Text Solution

    |

  20. Show that |{:(x,a,a),(a,x,a),(a,a,x):}|=(x+2a)(x-a)^2

    Text Solution

    |