Home
Class 12
MATHS
Let A=[[a,b],[c,d]] be a 2xx2 real matri...

Let `A=[[a,b],[c,d]]` be a `2xx2` real matrix. If `A-alphaI` is invertible for every real number `alpha` , then

A

`bc gt 0`

B

`bc =0`

C

`bc lt min (0,(1)/(2) ad)`

D

a=0

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. AIEEE /JEE Main Papers|71 Videos

  • MATHEMATICAL REASONING

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B. ARCHITECTURE ENTRANCE EXAMINATION PAPERS|11 Videos

  • PARABOLA

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTRE ENTRANCE EXAMINATION PAPERS|9 Videos

Similar Questions

Explore conceptually related problems

Let h(x) = Min. (x, x^(2)) , for every real number x, then

The matrix A=[[1,3,2],[1,x-1,1],[2,7,x-3]] will have inverse for every real number x except for

Let a,b,c d be real numbers such that for every natural number n. Then |a|+|b|+|c|+|d| is equal to

MCGROW HILL PUBLICATION-MATRICES-Questions from Previous Years. B -Architecture Entrance Examination Papers
  1. Let A =[(1,1,0),(0,1,0),(0,0,1)] and let I denote the 3xx3 identity ma...

    Text Solution

    |

  2. Let A and B be 2xx2 matrices with real entries . Let I be the 2xx2 ind...

    Text Solution

    |

  3. Let A=[[a,b],[c,d]] be a 2xx2 real matrix. If A-alphaI is invertible f...

    Text Solution

    |

  4. Let A be a 2xx2 matrix Statement -1 adj (adjA)=A Statement-2 abs(a...

    Text Solution

    |

  5. Let A=[(a,b),(c,d)]be a 2 xx 2 matrix, where a, b, c, d take value 0 t...

    Text Solution

    |

  6. Let S be the set of all real matrices A = [(a,b),(c,d)] such that a+d ...

    Text Solution

    |

  7. If S(n) denotes the sum of first n natural numbers.the [S(1)+S(2)x+S(3...

    Text Solution

    |

  8. Let A = [(1,1),(0,1)] and B = [(b(1),b(2)),(b(3),b(4))] . If 10 A^(10...

    Text Solution

    |

  9. If for a matrix A, absA=6and adj A={:[(1,-2,4),(4,1,1),(-1,k,0)]:}, th...

    Text Solution

    |

  10. Let S be the set of all real values of a for which the following syste...

    Text Solution

    |

  11. If A = ((2,52,152),(4,1-6,358),(6,162,620)) then the determinant of ad...

    Text Solution

    |

  12. Let S be the set of all real values of lambda for which the system of ...

    Text Solution

    |

  13. Ifthe equations a(y +z) =x,b(z+x) = y, c (x + y) = z have nontrivial...

    Text Solution

    |

  14. If B = [(-2,-2),(-1,0)] and A is a matrix such that A^(-1) B = B^(-1) ...

    Text Solution

    |

  15. Let [(3a,b,c),(b,3c,a),(c,a,3b)] be a 3xx3 matrix where a,b,c in R . I...

    Text Solution

    |

  16. The value of a for which the system linear of equations x+ay+z=1 a...

    Text Solution

    |

  17. Suppose A is a 2xx2 matrix for which A^(2)+A+I(2)=O(2) then det (adj (...

    Text Solution

    |

  18. If the system of linear equations : x+4y-3z=2 2x+7y+4z=alpha -x-...

    Text Solution

    |

  19. Let (a,b) be the solution of the system [(x,y)][(1,3),(5,1)]=[(2,1)]...

    Text Solution

    |

  20. If A^(20) = [(a,b),(c,d)] where A=[(1,1),(0,2)] then a+b+c+d is equal ...

    Text Solution

    |