Home
Class 12
MATHS
If A=[{:(2,3),(1,2):}], then prove that ...

If `A=[{:(2,3),(1,2):}]`, then prove that `A^(3)-4A^(2)+A=O`.

Promotional Banner

Topper's Solved these Questions

  • MATRICES

    ARIHANT PUBLICATION|Exercise ODISHA BUREAU .S TEXTBOOK SOLUTIONS (Exercise (b) )|43 Videos

  • LINEAR PROGRAMMING

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE (Long Answer Type Questions 6 Marks)|18 Videos

  • PROBABILITY

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE(LONG ANSWER TYPE QUESTIONS)|17 Videos

Similar Questions

Explore conceptually related problems

If A=[{:(3,1),(-1,2):}] then prove that A^(2)-5A+7I=O

If A=[{:(1,2,3),(3,-2,1),(4,2,1):}] then show that A^(3)-23A-40I=O

If A=[{:(3,sqrt(3),2),(4,2,0):}]andB=[{:(2,-1,2),(1,2,4):}] , then verify that (A')'=A

If A =[[1,2,2],[2,1,2],[2,2,1]] then prove that A^2-4A-5I=0 .

If A=[(1,2),(2,3),(3,4)]and B=[(2,3,0),(1,2,3)], then verify that (AB)^T=B^TA^T .

Let A=[{:(2,3),(-1,2):}]andf(x)=x^(2)-4x+7 . Show that f(A)=O. Use this result to find A^(5) .

If A=abs[[1,2,0],[1,1,0],[-1,4,0]],B=abs[[1,2,3],[1,1,-1],[4,-3,2]] and C= abs[[1,2,3],[1,1,-1],[2,2,2]] then prove that A(BC)=(AB)C

If [{:(9,-1,4),(-2,1,3),(1,2,-1):}]=A+[{:(1,2,-1),(0,4,9),(3,1,-2):}] , then find the matrix A .

ARIHANT PUBLICATION-MATRICES -CHAPTER PRACTICE (Very Short Answer Type Questions)
  1. Let A=[{:(2,3),(-1,2):}]andf(x)=x^(2)-4x+7 . Show that f(A)=O. Use thi...

    Text Solution

    |

  2. If A=[{:(2,0,1),(2,1,3),(1,-1,0):}] , then find A^(2)-5A+6I.

    Text Solution

    |

  3. If A=[{:(2,3),(1,2):}], then prove that A^(3)-4A^(2)+A=O.

    Text Solution

    |

  4. If A=[{:(1,0),(-1,7):}], thenfind k such that A^(2)-8A+kI=O.

    Text Solution

    |

  5. If A=[{:(3,-2),(4,-2):}], then find k such that A^(2)=kA-2I .

    Text Solution

    |

  6. For the matrix A=[{:(3,1),(7,5):}] , find a and b such that A^(2)+aI...

    Text Solution

    |

  7. Given that, A=[{:(4,0),(2k,5k):}] and B=[{:(k,0),(3,-1):}] such that A...

    Text Solution

    |

  8. A factory makes three products P,Q and R .The table shows the units of...

    Text Solution

    |

  9. A manufacturer sells the products x,y and z in two markets .Annual sal...

    Text Solution

    |

  10. A trust fund has Rs. 35000 is to be invested in two different types o...

    Text Solution

    |

  11. If AB= BA for any two square matrices , then prove by mathematical in...

    Text Solution

    |

  12. If A = diag [{:(a,b,c):}] , then show that A^(n)="diag"[{:(a^(n),b...

    Text Solution

    |

  13. If A=[{:(-1,2,3),(5,7,9),(-2,1,1):}]andB=[{:(-4,1,-5),(1,2,0),(1,3,1):...

    Text Solution

    |

  14. FIND (1)/(2)(A+A')and(1)/(2)(A-A') , where A=[{:(0,a,b),(-a,0,c),(-b,...

    Text Solution

    |

  15. Two shopkeepers A and B of a particular school have stock of books on ...

    Text Solution

    |

  16. Three schools A ,B and C want to award their selected students for ...

    Text Solution

    |

  17. If A=[{:(3,-4),(1,-1):}] , then show that (A-A') is a skew - symmetr...

    Text Solution

    |

  18. Show that the matrix B^(T) AB is symmetric or skew -symmetric , acco...

    Text Solution

    |

  19. Using elementary row transformation , find inverse of matrix A=[{:(6,...

    Text Solution

    |

  20. Find the inverse of matrix A=[{:(1,2,4),(-1,-2,-1),(2,1,-1):}] by ele...

    Text Solution

    |