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 x from the matrix equation [{:(1,3),(4,5):}][{:(x),(2):}]=[{:(5)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. If A=[{:(2,0,1),(2,1,3),(1,-1,0):}] then find the value of A^(2)-3A+2I

    Text Solution

    |

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

    Text Solution

    |

  6. If A=[[alpha,0],[1,1]] and B=[[1,0],[5,1]], show that for no values of...

    Text Solution

    |

  7. Find the inverse of the matrix [[0,0,2],[0,2,0],[2,0,0]].

    Text Solution

    |

  8. If A =[[1,-2,2],[3,1,-1]] B[[2,4],[1,2],[3,-1]] "verify" "that" (AB)^...

    Text Solution

    |

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

    Text Solution

    |

  10. [[1,-2],[3,2]][[x,2],[1,y]]=[[-3,4],[-1,4]]Find x and y.

    Text Solution

    |

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

    Text Solution

    |

  12. Find the inverse of the matrix [{:(2,5),(1,3):}]

    Text Solution

    |

  13. Find x, so that [{:(1,x,1):}][{:(1,3,2),(0,5,1),(0,3,2):}][{:(1),(1),(...

    Text Solution

    |

  14. Can the inverse of the following matrix be found? [[0,0,2],[3,6,0],[2,...

    Text Solution

    |

  15. Construct the matrix [a(ij)](2xx3) where a(ij)=|i-j|.

    Text Solution

    |

  16. If A=[[1,1],[2,2]] and B=[[2,1],[2,1]]find AB andBA.

    Text Solution

    |

  17. A and Bare square matrices of order n.Their product is commutative:Pro...

    Text Solution

    |

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

    Text Solution

    |

  19. If [[4x,x-2u],[2u+v,3v-2w]]=[[8,6],[3,5]] find x,u,v,w.

    Text Solution

    |

  20. Construct a matrix [a(ij)] of order 2xx2where a(ij)=i+2j.

    Text Solution

    |