Home
Class 12
MATHS
The matrix A=[[1,3,2],[1,x-1,1],[2,7,x-3...

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

A

`x=(11 +- sqrt(5))/(2)`

B

`x=(9 +- sqrt(5))/(2)`

C

`x=(11 +- sqrt(3))/(2)`

D

`x=(9 +- sqrt(3))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`A=[(1,3,2),(1,x-1,1),(2,7,x-3)]`
`|A|=1[(x-1)(x-3)-7]-3[(x-3)-2]+2[7-2(x-1)]`
`=x^(2)-11x+29=0`
If inverse will not exist then `|A|=0`
`x^(2)-11x+29=0`
`x=(11pmsqrt5)/(2)`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    NDA PREVIOUS YEARS|Exercise MCQ|59 Videos

  • PAIR OF STRAIGHT LINES

    NDA PREVIOUS YEARS|Exercise Example|12 Videos

Similar Questions

Explore conceptually related problems

[{:(1,-1),(2,3):}] find the inverse of matrix

The inverse of matrix [[1, -1], [2, 3]] is

[{:(1,3),(2,7):}] find the inverse of matrix

The inverse of the matrix [[1, 2, 3], [1, 1, 5], [2, 4, 7]] is

The value of x such that the matrix [[1,3,2],[2,5,x],[4,7-x,-6]] has no inverse is

The inverse of matrix [[1, 3], [2, 7]] is

For what value of x the matrix A=[[1,-2,3],[1,2,1],[x,2,-3]] is singular?

If [(1,-1,x),(1,x,1),(x,-1,1)] has no inverse, then the real value of x is

In the matrix A=[(3-2x,x+1),(2,4)] is singular then X=?

NDA PREVIOUS YEARS-MATRICES & DETERMINANTS-MQS
  1. The value of |{:(1," "1," "1),(1,1+x," "1),(1," "1,1+y):}|is

    Text Solution

    |

  2. If E(theta)=[[cos theta, sin theta] , [-sin theta, cos theta]] then E(...

    Text Solution

    |

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

    Text Solution

    |

  4. If the value of the determinants |(a,1,1),(1,b,1),(1,1,c)| is positive...

    Text Solution

    |

  5. Consider the following statements in respect of the determinant |[cos^...

    Text Solution

    |

  6. If A=[{:(1,0,-2),(2,-3,4):}], then the matrix X for which 2X + 3A = 0 ...

    Text Solution

    |

  7. If A=[{:(1,1,-1),(2,-3,4),(3,-2,3):}]and B=[{:(-1,-2,-1),(6,12,6),(5,1...

    Text Solution

    |

  8. If A is an invertible matrix of order n and k is any positive real num...

    Text Solution

    |

  9. If A is an orthogonal matrix of order 3 and B = [{:(1,2,3),(-3,0,2),(2...

    Text Solution

    |

  10. If a, b, c are real numbers, then the value the determinant |(1-a,a-...

    Text Solution

    |

  11. Cosider the function f(x)=|{:(x^(3),sin x,cos x),(6,-1,0),(p,p^(2),p^(...

    Text Solution

    |

  12. Cosider the function f(x)=|{:(x^(3),sin x,cos x),(6,-1,0),(p,p^(2),p^(...

    Text Solution

    |

  13. If A is a square matrix, then what is adj A^(T) - (adj A)^(T) equal to...

    Text Solution

    |

  14. Consider the following in respect of the matrix A=({:(-1,1),(1,-1):}):...

    Text Solution

    |

  15. Which of the following determinants have value 'zero'? 1. |{:(41,1,...

    Text Solution

    |

  16. The system of linear equations kx + y + z = 1, x + ky + z = 1 and x + ...

    Text Solution

    |

  17. If A is semy square matrix of order 3 and det A = 5, then what is det[...

    Text Solution

    |

  18. What is [x" "y" "z][{:(a,h,g),(h,b,f),(g,f,c):}]equal to ?

    Text Solution

    |

  19. Let ax^3+bx^2+cx+d =|(x+1,2x,3x),(2x+3,x+1,x), (2-x,3x+4,5x-1)| then w...

    Text Solution

    |

  20. Let ax^3+bx^2+cx+d =|(x+1,2x,3x),(2x+3,x+1,x), (2-x,3x+4,5x-1)| then w...

    Text Solution

    |