Home
Class 12
MATHS
Let A = [[1,-2,1],[-2,3,1],[1,1,5]] Veri...

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

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    PSEB|Exercise Exercise|101 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    PSEB|Exercise Exercise|151 Videos

  • DIFFERENTIAL EQUATIONS

    PSEB|Exercise Exercise|116 Videos

Similar Questions

Explore conceptually related problems

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

If A=[[1,2,2],[2,1,2],[2,2,1]] , verify that : A^2-4A-5I=O

Let A = [[3,7],[2,5]] and B = [[6,8],[7,9]] Verify that (AB)^-1 = B^-1A^-1

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

Find the adjoint of the matrix A = [(4,-6,1),(-1,-1,1),(-4,11,-1)] and verify that A(adj A) = (adj A ) A = |A | I_3

If A = [[1,3,3],[1,4,3],[1,3,4]] , then verify that A. adj A = |A|I. Also find A^-1 .

If A = [[3,2,-3],[2,-1,1],[4,3,2]] then find A(adj A)

If A=[(1,2,5),(2,3,1),(-1,1,1)] verify that A^(-1)A="AA"^(-1)=I

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

If A= [(1,-1,1),(2,-1,0),(1,0,0)] and B = [(1,3,2),(1,1,1),(2,-3,-1)] , verify that (AB)^-1 = B^-1 A^-1

PSEB-DETERMINANTS-Exercise
  1. Prove that the determinant |[x,sintheta,costheta],[-sintheta,-x,1],[co...

    Text Solution

    |

  2. Without expanding the determinant, prove that |[a,a^2,bc],[b,b^2,ca],[...

    Text Solution

    |

  3. Evaluate |[cosalphacosbeta,cosalphasinbeta,-sinalpha],[-sinbeta,cosbet...

    Text Solution

    |

  4. If a, b and c are real numbers, and triangle = |[b+c,c+a,a+b],[c+a,a+b...

    Text Solution

    |

  5. Solve the equation |[x+a,x,x],[x,x+a,x],[x,x,x+a]| = 0 a ne 0

    Text Solution

    |

  6. Prove that: |[a^2,bc,ac+c^2],[a^2+ab,b^2,ac],[ab,b^2+bc,c^2]|=4a^2b^2c...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. Evaluate |[x,y,x+y],[y,x+y,x],[x+y,x,y]|

    Text Solution

    |

  11. Evaluate |[1,x,y],[1,x+y,y],[1,x,x+y]|

    Text Solution

    |

  12. Using properties of determinants, prove that: |[alpha,alpha^2,beta+gam...

    Text Solution

    |

  13. Using properties of determinants, prove that: |[x,x^2,1+px^3],[y,y^2,1...

    Text Solution

    |

  14. Using properties of determinants, prove that: |[3a,-a+b,-a+c],[-b+a,3b...

    Text Solution

    |

  15. Prove that: |[1,1+p,1+p+q],[2,3+2p,4+3p+2q],[3,6+3p,10+6p+3q]|=1

    Text Solution

    |

  16. Using properties of determinants, prove that: |[sinalpha,cosalpha,cos(...

    Text Solution

    |

  17. Solve the system of equations: 2/x+3/y+10/z = 4, 4/x-6/y+5/z = 1, 6/x+...

    Text Solution

    |

  18. If a, b, c, are in A.P, then the determinant |[x+2,x+3,x+2a],[x+3,x+4,...

    Text Solution

    |

  19. If x. y, z are non- real number", then the inverse of matrix A = [[x,0...

    Text Solution

    |

  20. Let A = [[1,sintheta,1],[-sintheta,1,sintheta],[-1,-sintheta,1]], wher...

    Text Solution

    |