Home
Class 12
MATHS
Verify that A=[[a,b],[c,d]] satisfies ...

Verify that `A=[[a,b],[c,d]]`
satisfies the equation `A^2-(a+d)A+(ad-bc) I=0` where `I` is the `2`x`2` unit matrix.

Promotional Banner

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    SHARAM PUBLICATION|Exercise EXAMPLE|37 Videos

  • MODEL QUESTION PAPER -1

    SHARAM PUBLICATION|Exercise EXERCISE|41 Videos

Similar Questions

Explore conceptually related problems

Show that the matrix A=[[2,3,],[1,2,]] satisfies the equation A^2-4A+I=O where I is a 2xx2 identity matrix and O is 2xx2 zero matrix.Using this equation.find A^-1 .

Verify that |P({a,b,c})|=2^3

Write the solution of the equation (d^2y)/(dx^2)=0

For the matrix A=[{:(3,1),(7,5):}] , find a and b such that A^(2)+aI=bA , where I is a 2xx2 identity matrix .

If A= [[ 3,-5,],[-4,2,]] ,show that A^2-5A-14I=O, where I is a unit matrix of Oder 2.

If the equation of x-axis is x/a=(y-d)/(b)=z/c , what is the value of a,b,c,d?

Show that A =((2,-3)(3,4)) satisfies equation x^2-6x+17=0 . Hence find A^-1 .

If A= [[4,2],[-1,1]] and I be the 2xx2 unit matrix find (A-2I)(A-3I)

SHARAM PUBLICATION-MATRICES-EXAMPLE
  1. Find the matrix which when added to [[2,-3],[-4,7]] gives [[4,-1],[3,2...

    Text Solution

    |

  2. IF [[x1,x2],[y1,y2]]-[[2,3],[0,1]]=[[3,5],[1,2]] then determine x1,x2,...

    Text Solution

    |

  3. Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc...

    Text Solution

    |

  4. Using elementary transformation find the inverse of the matrix [[1,3],...

    Text Solution

    |

  5. Using elementary operation,find the inverse of [[4,5],[3,4]].

    Text Solution

    |

  6. If A=[[1,-2,1],[0,-1,1],[2,0,-3]]then find A^(-1) and hence solve the ...

    Text Solution

    |

  7. Find the value of x,y, and z if A=[[0,2y,z],[x,y,-z],[x,-y,z]] satisfi...

    Text Solution

    |

  8. Find the matrix A such that [[2,-1],[1,0],[-3,4]]A = [[-1,-8,-10],[...

    Text Solution

    |

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

    Text Solution

    |

  10. Findthe inverse ofthe matrix[[1,1,2],[0,1,2],[1,2,1]].

    Text Solution

    |

  11. Matrices X and Y are such that 3X + 4Y = I and X-2Y = 2I where I deno...

    Text Solution

    |

  12. Find the inverse of the matrix[[1,2,3],[2,1,4],[1,0,2]].

    Text Solution

    |

  13. Find x,y if[[3,2],[7,x]][[5,-2],[-7,y]]=[[1,0],[0,1]].

    Text Solution

    |

  14. If A=[[2,1],[1,2]],B=[[3,2],[2,1]] find (AB)^(-1).

    Text Solution

    |

  15. Find the adjoint of the matrix [[1,1,2],[0,1,2],[1,2,1]].

    Text Solution

    |

  16. Verify that (AB)^(T) =B^(T)A^(T) where A=|[1,-2,2],[3,1,-1]| and B=|[...

    Text Solution

    |

  17. If A=[[1,1],[-1,-1]], B=[[-1,3],[-3,1]] then show that (A+B)^2 !=A^2 +...

    Text Solution

    |

  18. There are two families A and B. There are 4 men, 6 women and 2 childre...

    Text Solution

    |

  19. Find the inverse of the matrix [{:(4,-2),(3,1):}]

    Text Solution

    |

  20. solve 3x - 2y + z = 1 2x + y- 5z = 2 x- y - 2z = 3.

    Text Solution

    |