Home
Class 12
MATHS
For the matrix A = [[3,2],[1,1]], find t...

For the matrix `A = [[3,2],[1,1]]`, find the numbers a and b such that `A^2+aA+bI = O`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MODERN PUBLICATION|Exercise EXERCISE|326 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE|588 Videos

  • EXCLUSIVELY FOR JEE(ADVANCED)

    MODERN PUBLICATION|Exercise EXERCISE|38 Videos

Similar Questions

Explore conceptually related problems

for the matrix A= [(3,2),(1,1),], find x and y such that A^2+xA+yI=0 .

If A = {:[(3,2),(1,1)] , find a and b for which A^2 + aA + bI = O

IF (A=[[3,-4],[-1,2]]) , find a matrix B such thet (AB = 1)

Find the adjoint of the matrix A=[[1,2,2],[2,1,2],[2,2,1]] and hence show that A(a d j\ A)=|A|\ I_3 .

Find the inverse of the matrix A = [[a,b],[c, frac{1+bc}{a}]] and show that: aA^-1 = (a^2 + bc + 1) I - aA.

Find adjoint of the matrix: [[1,2],[3,4]

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

Find the adjoint of the matrix A = [(-1,-2,-2),(2,1,-2),(2,-2,1)] and hence show that A (AdjA) = |A | I_3

MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Show that the matrix A = [[2,3],[1,2]satisfies the equation A^2-4A+I =...

    Text Solution

    |

  2. If A = [[3,1],[-1,2]], show thatA^2-5A +7I = O

    Text Solution

    |

  3. For the matrix A = [[3,2],[1,1]], find the numbers a and b such that A...

    Text Solution

    |

  4. If A=[(2,-3),(-4,7)] compute A^(-1) and show that 2A^(-1) + A-9I =0

    Text Solution

    |

  5. If A= {:[(6,7),(8,9)] and B = {:[(3,2),(7,5)], find (AB)^-1

    Text Solution

    |

  6. Find the inverse of each of the following: {:[(1,-1,2),(0,2,-3),(3,-...

    Text Solution

    |

  7. Find the inverse of each of the following: {:[(1,2,3),(0,2,4),(0,0,5...

    Text Solution

    |

  8. Find the inverse of each of the following: {:[(2,1,3),(4,-1,0),(-7,2...

    Text Solution

    |

  9. Find the inverse of each of the following: {:[(1,0,0),(3,3,0),(5,2,-...

    Text Solution

    |

  10. If P = {:[(1,2,-2),(-1,3,0),(0,-2,1)], find P^-1. Verify that PP^-1= I...

    Text Solution

    |

  11. Compute (AB)^(-1) , where A=[(5,0,4),(2,3,2),(1,2,1)],B^(-1)=[(1,2,3),...

    Text Solution

    |

  12. If A={:[(1,2,2),(2,1,2),(2,2,1)], prove thst A^2-4A-5I = O and hence,...

    Text Solution

    |

  13. If A = [[2,-1,1],[-1,2,-1],[1,-1,2]], Verify that A^3-6A^2+9A-4I=O and...

    Text Solution

    |

  14. If A^-1 = [[3,-1,1],[-15,6,-5],[5,-2,2]] and B = [[1,2,-2],[-1,3,0],[0...

    Text Solution

    |

  15. Let A = [[1,-2,1],[-2,3,1],[1,1,5]] Verify that [adj A]^-1 = adj (A^-1...

    Text Solution

    |

  16. Let A = [[1,-2,1],[-2,3,1],[1,1,5]] Verify that (A^-1)^-1 = A

    Text Solution

    |

  17. Find |A|: A = {:[(1,-2,2),(2,3,5),(-2,0,1)]

    Text Solution

    |

  18. Verify A(adj A) = (adj A).A = |A|.I : [[1,-1,2],[3,0,-2],[1,0,3]]

    Text Solution

    |

  19. Find |A|: A = {:[(2,1,5),(3,-2,-4),(-3,1,-2)]

    Text Solution

    |

  20. Find the inverse of the matrix : A = {:[(a,b),(c,(1+bc)/a)].

    Text Solution

    |