Home
Class 12
MATHS
Find the inverse of each of the matrices...

Find the inverse of each of the matrices given below :
Let `D= "diag" [d_(1),d_(2),d_(3)]` where none of `d_(1),d_(2),d_(3)` is ), prove that
`D^(-1)="diag" [d_(1)^(-1),d_(2)^(-1),d_(3)^(-1)]`.

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Check your understanding|10 Videos
  • DETERMINANTS

    MODERN PUBLICATION|Exercise Competition file|14 Videos
  • DETERMINANTS

    MODERN PUBLICATION|Exercise Exercise|4 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos
  • DIFFERENTIAL EQUATIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST (9)|12 Videos

Similar Questions

Explore conceptually related problems

Statement 1: if D=diag[d_(1),d_(2),,d_(n)], then D^(-1)=diag[d_(1)^(-1),d_(2)^(-1),...,d_(n)^(-1)] Statement 2: if D=diag[d_(1),d_(2),,d_(n)], then D^(n)=diag[d_(1)^(n),d_(2)^(n),...,d_(n)^(n)]

If D=diag(d_1,d_2,d_3,…,d_n)" where "d ne 0" for all " I = 1,2,…,n," then " D^(-1) is equal to

If D=diag[d_(1),d_(2),...d_(n)], then prove that f(D)=diag[f(d_(1)),f(d_(2)),...,f(d_(n))], where f(x) is a polynomial with scalar coefficient.

If D=diag [2, 3, 4] , then D^(-1)=

Let d_(1),d_(2),d_(3),......,d_(k) be all the divisors of a positive integer n including 1 and n. Suppose d_(1)+d_(2)+d_(3)+......+d_(k)=72, then the value of (1)/(d_(1))+(1)/(d_(2))+(1)/(d_(3))+......+(1)/(d_(k)) is

MODERN PUBLICATION-DETERMINANTS-Revision Exercise
  1. Solve for x in R : |((x+a)(x-a),(x+b)(x-b),(x+c)(x-c)),((x-a)^3,(x-b)...

    Text Solution

    |

  2. If a,b,c are in A.P. find the value of: ||2y+4, 5y+7, 8y+a],[3y+5, 6y+...

    Text Solution

    |

  3. If ax^(2)+2hxy+by^(2)+2gx+2fy+c-=(lx+my+n)(l'x+m'y+n'), then prove tha...

    Text Solution

    |

  4. If a+b+c=0 and |[a-x,c,b],[c,b-x,a],[b,a,c-x]|=0 then x=

    Text Solution

    |

  5. If A+B+C=pi, then value of |{:(sin(A+B+C),sinB,cosC),(-sinB,0,tanA),(c...

    Text Solution

    |

  6. Using properties of determinants. Prove that |xx^2 1+p x^3y y^2 1+p y^...

    Text Solution

    |

  7. If A=[[3,-3,4],[2,-3,4],[0,-1,1]] , then

    Text Solution

    |

  8. If A=[{:(3,-3,4),(2,-3,4),(0,-1,1):}], then show that A^(3)=A^(-1).

    Text Solution

    |

  9. If A=[1tanx-tanx1] , show that A^T\ A^(-1)=[cos2x-sin2xsin2xcos2x] .

    Text Solution

    |

  10. If A=[(2,-3),(4,6)] " verify that " (adj A)^(-1)=(adj A^(-1)).

    Text Solution

    |

  11. Prove that : adj. I(n)=I(n)

    Text Solution

    |

  12. Prove that : adj.O=O

    Text Solution

    |

  13. Prove that : I(n)^(-1)=I(n)

    Text Solution

    |

  14. Find the inverse of each of the matrices given below : Let D= "dia...

    Text Solution

    |

  15. Let F(alpha)=[{:(cosalpha,-sinalpha,0),(sinalpha,cosalpha,0),(0,0,1):}...

    Text Solution

    |

  16. Find the inverse of each of the matrices given below : Obtain the in...

    Text Solution

    |

  17. Use product [1-1 2 0 2-3 3-2 4]\ \ [-2 0 1 9 2-3 6 1-2] to solve th...

    Text Solution

    |

  18. If a!=p ,b!=q ,c!=ra n d|p b c a q c a b r|=0, then find the value of ...

    Text Solution

    |

  19. Suppose that digit numbers A28,3B9 and 62 C, where A,B and C are integ...

    Text Solution

    |

  20. let a > 0 , d > 0 find the value of the determinant |[1/a,1/(a(a + d))...

    Text Solution

    |