Home
Class 12
MATHS
If A=[{:(1,2),(4,1):}], find A^(2)+2A+7I...

If `A=[{:(1,2),(4,1):}]`, find `A^(2)+2A+7I`.

Text Solution

Verified by Experts

The correct Answer is:
`=[{:(18,8),(16,18):}]`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Long Answer Type Questions)|4 Videos

  • MATRICES

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Objective type Questions)|15 Videos

  • MATRICES

    KUMAR PRAKASHAN|Exercise TEXTBOOK ILLUSTRATIONS FOR PRACTICE WORK |28 Videos

  • LINEAR PROGRAMMING

    KUMAR PRAKASHAN|Exercise PRACTICE WORK|25 Videos

  • PROBABILITY

    KUMAR PRAKASHAN|Exercise Practice Paper - 13 (Section - D (Answer the following questions))|2 Videos

Similar Questions

Explore conceptually related problems

Prove that : A^(2)-6A+17I_(2)=0 . When A=[{:(2,-3),(3,4):}] Also find A^(-1) .

If A=[{:(3,-2),(4,-2):}]andI=[{:(1,0),(0,1):}] , find k so that A^(2)=kA-2I .

If A=[{:(1,0),(-1,7):}]andA^(2)=8A+KI then find K.

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

If A=[{:(3,1),(-1,2):}] show that A^2-5A+7I=O . Hence find A^(-1)

If A=[{:(1,2),(4,1),(5,6):}],B=[{:(1,2),(6,4),(7,3):}] , then verify that : (i) (2A+B)=2A'+B' (ii) (A-B)'=A'-B'

If X=[{:(3,1,-1),(5,-2,-3):}]andY=[{:(2,1,-1),(7,2,4):}] , find (i) X+Y (ii) 2X-3Y (iii) A matrix Z such that X+Y +Z is a zero matrix.

If A=[1,7] and B=[{:(2,1),(3,4):}] , then find AB.

If A=[{:(1,-1),(0,2),(2,3):}]andB=[{:(1,0),(-1,7):}] then find AB. Also find BA if it exists ?

KUMAR PRAKASHAN-MATRICES -Solutions of NCERT Exemplar Problems (Short Answer Type Questions)
  1. Show that A'A and A A ' are both symmetric matrices for any matrix A .

    Text Solution

    |

  2. Let A and B be square matrices of the order 3xx3 . Is (AB)^(2)=A^(2)B^...

    Text Solution

    |

  3. Show that if A and B are square matrics such that AB=BA , then (A+B)^(...

    Text Solution

    |

  4. Let A=[{:(1,2),(-1,3):}],B=[{:(4,0),(1,5):}],C=[{:(2,0),(1,-2):}]and a...

    Text Solution

    |

  5. If A=[{:(cosq,sinq),(-sinq,cosq):}] , then show that A^(2)=[{:(cos(2q...

    Text Solution

    |

  6. If A=[{:(0,-x),(x,0):}],B=[{:(0,1),(1,0):}]andx^(2)=-1 then show that ...

    Text Solution

    |

  7. Verify that A^(2)=I when A=[{:(0,1,-1),(4,-3,4),(3,-3,4):}].

    Text Solution

    |

  8. Prove by Mathematical Induction that (A)^(n)=(A^(n)) where n inN for a...

    Text Solution

    |

  9. Find inverse , by elementary row operations (if possible), of the foll...

    Text Solution

    |

  10. If [{:(xy,4),(z+6,x+y):}]=[{:(8,w),(0,6):}] , then find values of x,y,...

    Text Solution

    |

  11. If A=[{:(1,5),(7,12):}],B=[{:(9,1),(7,8):}] find a matrix C such that ...

    Text Solution

    |

  12. If A=[{:(3,-5),(-4,2):}], then find A^(2)-5A-14I. Hence , obtain A^(3)...

    Text Solution

    |

  13. Find the values of a,b ,c and d, if 3[{:(a,b),(c,d):}]=[{:(a,6),(-1,...

    Text Solution

    |

  14. Find the matrix X such that , [{:(2,-1),(1,0),(-3,4):}]X=[{:(-1,-8...

    Text Solution

    |

  15. If A=[{:(1,2),(4,1):}], find A^(2)+2A+7I.

    Text Solution

    |

  16. If A=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}],andA^(-1)=A', find...

    Text Solution

    |

  17. If the maxtrix [{:(0,a,3),(2,b,-1),(c,1,0):}] is a skew symmetric mat...

    Text Solution

    |

  18. If p(x)=[{:(cosx,sinx),(-sinx,cosx):}] then show that p(x)*p(y)=p(x+y)...

    Text Solution

    |

  19. If A is square matrix such that A^(2)=A, show that (I+A)^(3)=7A+I.

    Text Solution

    |

  20. If A,B are square matrices of same order and B is a skew -symmetric ma...

    Text Solution

    |