Home
Class 12
MATHS
If A=(1)/(3)[{:(1,2,2),(2,1,-2),(-2,2,-1...

If `A=(1)/(3)[{:(1,2,2),(2,1,-2),(-2,2,-1):}]` then show that A A'=A'A=I.

Promotional Banner

Topper's Solved these Questions

  • MATRICES

    KUMAR PRAKASHAN|Exercise TEXTBOOK BASED MCQS|43 Videos

  • MATRICES

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

  • MATRICES

    KUMAR PRAKASHAN|Exercise MISCELLANEOUS EXERCISE -3|15 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

If A=[{:(-1,2,0),(-1,1,1),(0,1,0):}] then show that A^(-1)=A^2

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

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

For the matrix A=[{:(1,2,2),(2,1,2),(2,2,1):}] . Show that A^2-4A-5I=0 Hence find A^(-1)

If A=[{:(1,0,-1),(2,1,3),(0,1,1):}] , then verify that A^(2)+A=A(A+I) where I is 3xx3 unit matrix.

If A=[{:(1,2,1),(2,1,3),(1,1,0):}] then prove that A^3-2A^2-7A-4I_3=0 . Hence find A^(-1)

If A=[{:(1,0,2),(0,2,1),(2,0,3):}] then , prove that A^(3)-6A^(2)+7A+2I=O .

If the inverse of the matrix A=[{:(1,2,2),(2-1,,2),(2,2,1):}]"is"(1)/(5)[{:(-3,2,2),(2,-3,alpha),(2,2-3,):}] then , alpha= _________

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

KUMAR PRAKASHAN-MATRICES -PRACTICE WORK
  1. A=[{:(5,-1),(6,7):}],B=[{:(2,1),(3,4):}]andC=[{:(1,3),(-1,4):}] then ...

    Text Solution

    |

  2. A=[{:(2,3,-1),(1,-2,4):}]andB=[{:(1,4),(2,5),(-1,3):}] then verify tha...

    Text Solution

    |

  3. If A=(1)/(3)[{:(1,2,2),(2,1,-2),(-2,2,-1):}] then show that A A'=A'A=...

    Text Solution

    |

  4. If A=[{:(1,2,5),(5,1,1),(3,0,4):}] then find A-2A'.

    Text Solution

    |

  5. For the matrices A and B, verify that (AB)'=B'A. (i) A=[{:(1),(3),...

    Text Solution

    |

  6. Express the matrix B=[{:(2,-2,-4),(-1,3,4),(1,-2,-3):}] as the sum of...

    Text Solution

    |

  7. Show that all the diagonals elements of a skew symmetric matrix are ze...

    Text Solution

    |

  8. Prove that if A is a square matrix then ,(i) (A+A') is a symmetric met...

    Text Solution

    |

  9. Express the matrix A=[{:(2,3,4),(5,6,-2),(1,4,5):}] as the sum of a s...

    Text Solution

    |

  10. If a matrix A is a symmetric matrix then show that A^(n) is also a sy...

    Text Solution

    |

  11. Using elementary transformations find the inverse of each of the follo...

    Text Solution

    |

  12. Find the inverse of [{:(7,4),(1,-2):}]

    Text Solution

    |

  13. Find the inverse of each of the following matrices [{:(-1,2),(-3,5):}...

    Text Solution

    |

  14. Find adjoint of each of the matrices [{:(0,1,2),(1,2,3),(3,1,1):}]

    Text Solution

    |

  15. Find inverse of [{:(1,2,1),(3,2,3),(1,1,2):}]

    Text Solution

    |

  16. If A=[{:(costheta,sintheta),(-sintheta,costheta):}] then prove that ...

    Text Solution

    |

  17. Find the matrix X such that , X[{:(5,-7),(-2,3):}]=[{:(-16,-6),(7,2)...

    Text Solution

    |

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

    Text Solution

    |

  19. Find x, if [1" "x" "1][{:(1,3,2),(2,5,1),(15,3,2):}][{:(1),(2),(x):}]=...

    Text Solution

    |

  20. Find the real numbers x and y so that (xI+yA)^(2)=A, where A=[{:(0,1),...

    Text Solution

    |