Home
Class 12
MATHS
If A = [[1,0,1],[0,1,2],[0,0,4]] then s...

If `A = [[1,0,1],[0,1,2],[0,0,4]]` then show that `|3A| = 27|A|`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    PRADEEP PUBLICATION|Exercise EXERCISE|342 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    PRADEEP PUBLICATION|Exercise EXERCISE|788 Videos

  • DIFFERENTIAL EQUATIONS

    PRADEEP PUBLICATION|Exercise EXERCISE|507 Videos

Similar Questions

Explore conceptually related problems

If A=[[3,-3,4],[2,-3,4],[0,-1,1]] , then

If A= [3,2,0],[1,4,0][0,0,5] , then show that A^2 −7A+10I3 =0

If A = [[2,0,1],[2,-1,3],[1,1,0]] then find A^2-3A+2I .

If A = [(-1,2,0),(-1,1,1),(0,1,0)] , show that A^2 = A^-1

If A=[[2,0,-1],[5,1,0],[0,1,3]] , prove that : A^-1=A^2-6A+11I

If A = {:[(3,1,-1),(0,1,2)] , then show that AA' is a symmetric matrix.

If A= [[5,2],[-1,2]] and I= [[1,0],[0,1]] show that (A-3I) (A-4I)=0

If A=|(3,-1,-2),(0,0,-1),(3,-5,0)| , show that |2A| = 8|A|

If Matrix A= [[2,-1],[3,2]] , then show that A^2-4A+7I=0 and hence find A^-1 from this equation.

If A= [[6,2],[-1,3]] and I= [[1,0],[0,1]] show that (A-4I) (A-5I)=0

PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. Evaluate the following determinants: {:|(x^2-x+1,x-1),(x+1,x+1)|

    Text Solution

    |

  2. If A =[{:(1,2),(4,2):}], then show that | 2A| = 4|A|.

    Text Solution

    |

  3. If A = [[1,0,1],[0,1,2],[0,0,4]] then show that |3A| = 27|A|

    Text Solution

    |

  4. Evaluate the following determinants: {:|(3,-1,-2),(0,0,-1),(3,-5,0)|

    Text Solution

    |

  5. Evaluate the determinant : |[3,-4,5],[1,1,-2],[2,3,1]|

    Text Solution

    |

  6. Evaluate the determinant : |[0,1,2],[-1,0,-3],[-2,3,0]|

    Text Solution

    |

  7. Evaluate the determinant Delta = abs{:(2,-1,-2),(0,2,-1),(3,-5,0):}.

    Text Solution

    |

  8. If A = [{:(1,1,-2),(2,1,-3),(5,3,-9):}], find |A|.

    Text Solution

    |

  9. Find values of x, if : |[2,4],[5,1]| = |[2x,4],[6,x]|

    Text Solution

    |

  10. Find the value of x, if |{:(2,3),(4,5):}|=|{:(x,3),(2x,5):}|.

    Text Solution

    |

  11. If |[x,2],[18,x]| = |[6,2],[18,6]|, then x is equal to:

    Text Solution

    |

  12. Using the property of determinants and without expanding , prove that:...

    Text Solution

    |

  13. Using the property of determinants and without expanding , prove that:...

    Text Solution

    |

  14. Using the property of determinants and without expanding , prove that:...

    Text Solution

    |

  15. Using the property of determinants and without expanding , prove that:...

    Text Solution

    |

  16. Using the property of determinants and without expanding prove that : ...

    Text Solution

    |

  17. By using properties of determinants, Show that : {:|(0,a,-b),(-a,0,-...

    Text Solution

    |

  18. Prove that: |[-a^2, ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2

    Text Solution

    |

  19. By using properties of determinants, show that : |[1,a,a^2],[1,b,b^2]...

    Text Solution

    |

  20. By using properties of determinants, show that : |[1,1,1],[a,b,c],[a^...

    Text Solution

    |