Home
Class 12
MATHS
If A is a 2xx2 matrix such that A^(2)-4A...

If A is a `2xx2` matrix such that `A^(2)-4A+3I=O`, then prove that `(A+3I)^(-1)=7/24 I-1/24 A`.

Text Solution

Verified by Experts

We have, `A^(2)-4A+3I=O`
`implies A(A+3I)-7A+3I=O`
`implies A(A+3I)-7(A+3I)=-24 I`
`implies (A+3I) (A-7I)=-24 I`
`implies (A+3I) (7/24 I-A/24)=I`
`implies (A+3 I)^(-1) =7/24 I- A/24`
Promotional Banner

Topper's Solved these Questions

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

If A^(3)=O , then prove that (I-A)^(-1) =I+A+A^(2) .

If A is a matrix of size nxxn such that A^(2) + A + 2I = O then

If A be a 2 times 2 matrix such that A^(2)=A , then show that (I-A)^(2)=I-A where I is the unit matrix of order 2 times 2 .

If A is a square matrix such that A^(2)= I , then (A-I)^(3)+(A+I)^(3)-7A is equal to

If A is a square matrix such that A^(2)=A, then (I+A)^(3)-7A is equal to___

If A is a square matrix such that A^2=A , then write the value of 7A-(I+A)^3, where I is the identity matrix.

Let A be a matrix of order 2xx2 such that A^(2)=O . (I+A)^(100) =

Let a be a matrix of order 2xx2 such that A^(2)=O . (I+A)^(100) =

If A=[(3,1),(-1,2)] , show that A^(2)-5A+7I=0 .

CENGAGE PUBLICATION-MATRICES-All Questions
  1. If A =[[cos alpha,-sin alpha],[sinalpha, cos alpha]] , B= [[cos 2 beta...

    Text Solution

    |

  2. If A=[(1,2,2),(2,2,3),(1,-1,3)], C=[(2,1,1),(2,2,1),(1,1,1)], D=[(10),...

    Text Solution

    |

  3. If A is a 2xx2 matrix such that A^(2)-4A+3I=O, then prove that (A+3I)^...

    Text Solution

    |

  4. For two unimobular complex numbers z(1) and z(2), find [(bar(z)(1),-z(...

    Text Solution

    |

  5. Prove that inverse of a skew-symmetric matrix (if it exists) is skew-s...

    Text Solution

    |

  6. If square matrix a is orthogonal, then prove that its inverse is also ...

    Text Solution

    |

  7. If A is a skew symmetric matrix, then B=(I-A)(I+A)^(-1) is (where I is...

    Text Solution

    |

  8. Prove that ("adj. "A)^(-1)=("adj. "A^(-1)).

    Text Solution

    |

  9. Using elementary transformation, find the inverse of the matrix A=[(a,...

    Text Solution

    |

  10. If A and P are the square matrices of the same order and if P be inver...

    Text Solution

    |

  11. Show that the characteristics roots of an idempotent matrix are either...

    Text Solution

    |

  12. If alpha is a characteristic root of a nonsin-gular matrix, then prove...

    Text Solution

    |

  13. If A is symmetric as well as skew-symmetric matrix, then A is

    Text Solution

    |

  14. Elements of a matrix A or orddr 10xx10 are defined as a(i j)=w^(i+j) (...

    Text Solution

    |

  15. If A1, A2, , A(2n-1)a r en skew-symmetric matrices of same order, the...

    Text Solution

    |

  16. The equation [1 x y][(1,3,1),(0,2,-1),(0,0,1)] [(1),(x),(y)]=[0] has ...

    Text Solution

    |

  17. Let Aa n dB be two 2xx2 matrices. Consider the statements (i) A B=O =>...

    Text Solution

    |

  18. The number of diagonal matrix, A or ordern which A^3=A is a. is a a. 1...

    Text Solution

    |

  19. A is a 2xx2 matrix such that A[[1],[-1]]=[[-1],[ 2]] and A^2[[1],[-1]]...

    Text Solution

    |

  20. If theta-phi=pi/2, prove that, [(cos^2 theta,cos theta sin theta),(cos...

    Text Solution

    |