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

  • MATRICES

    CENGAGE|Exercise Exercise (Single)|65 Videos

  • MATRICES

    CENGAGE|Exercise Exercise (Multiple)|33 Videos

  • MATRICES

    CENGAGE|Exercise Exercise 13.4|12 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Single Correct Answer Type|46 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 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)=1 then (A-I)^(3)+(A+I)^(3)-7A is equal to

If A=[42-11], prove that (A-2I)(A-3I)=O

If a matrix A is such that 4A^(3)+2A^(2)+7A+I=0 , then A^(-1) equals

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

If A=[3-24-2] and I=[1001], then prove that A^(2)-A+2I=O

If A={:((1,2),(3,4)):} and X is a 2 xx2 matrix such that AX = I , find X.

CENGAGE-MATRICES-Exercise 13.5
  1. By the method of matrix inversion, solve the system. [(1,1,1),(2,5,7...

    Text Solution

    |

  2. Let A=[[2,0,7] , [0,1,0], [1,-2,1]] and B=[[-x,14x,7x] , [0,1,0] , [x,...

    Text Solution

    |

  3. Find A^(-1) if A=|(0,1,1),(1,0,1),(1,1,0)| and show that A^(-1)=(A^(2)...

    Text Solution

    |

  4. For the matrix A=[3 1 7 5] , find x and y so that A^2+x I=y Adot

    Text Solution

    |

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

    Text Solution

    |

  6. If A=[[cos alpha, -sin alpha] , [sin alpha, cos alpha]], B=[[cos2beta,...

    Text Solution

    |

  7. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. Show that the two matrices A, P^(-1) AP have the same characteristic r...

    Text Solution

    |

  16. Show that the characteristics roots of an idempotent matris are either...

    Text Solution

    |

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

    Text Solution

    |