Home
Class 12
MATHS
First row of a matrix A is [1,3,2]. If ...

First row of a matrix A is `[1,3,2]`. If
adj `A=[(-2,4,alpha),(-1,2,1),(3alpha,-5,-2)]`, then a det (A) is

A

`-2`

B

`-1`

C

0

D

1

Text Solution

Verified by Experts

We know that
det `(A)=a_(11)A_(11)+a_(12)A_(21)+a_(13)A_(31)`
`=(1) (-2)+(3) (-1)+(2) (3alpha)`
`= 6 alpha-5`
Also, `("det. (A)")^(2)=` det. (adj. A) `=-10+17 alpha-6 alpha^(2)`
`:. (6 alpha-5)^(2)=-10+17 alpha-6 alpha^(2)`
`implies 42 alpha^(2)-77alpha+35=0`
`implies 6alpha^(2)-11alpha+5=0`
`implies (alpha-1) (6alpha-5)=0`
`implies alpha=1, 5//6`
For `alpha=1`, det (A) `=6-5=1`
For `alpha=5//6`, det `(A)=0`
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,-3,4),(2,-3,4),(0,-1,1):}] , then the trace of the matrix Adj(AdjA) is

If A = [(2,5,3),(3,1,2),(1,2,-1)] be a square matrix, find Adj.A and A^(-1)

By row transformation find inverse of the matrix A= [[1,3,2],[-3,-3,-1],[2,1,0]]

Find adj A for A = {:[( 2,3),( 1,4) ]:}

If a matrix A = (alpha_(i_j))_(3xx4) and alpha(i_j) = (-1)^(hati + hatj) , then the element fo 3rd row and 2nd column will be

If A and B are two non-singular matrices of order 3 such that A A^(T)=2I and A^(-1)=A^(T)-A . Adj. (2B^(-1)) , then det. (B) is equal to

Prove that the maximum value of (cos alpha_(1)) (cos alpha_(2))...( cos alpha_(r)) uder the restrictions 0 le alpha_(r) le (pi)/(2) (r=1, 2,..., n) and (cot alpha_(1)) (cot alpha_(2))...( cot alpha_(r))=1 "is" (1)/(2^(n/2))

Let A be a square matrix of order 3 such that det. (A)=1/3 , then the value of det. ("adj. "A^(-1)) is

Let A =[(1,-1,1),(2,1,-3),(1,1,1)] and 10B=[(4,2,2),(-5,0,alpha),(1,-2,3)] . If B is the inverse of A, then find the value of alpha

Using elementary row transfromations find the inverse of matrix: [(1,2,3),(2,5,7),(-2,-4,-5)]

CENGAGE PUBLICATION-MATRICES-All Questions
  1. Let A and B be square matrices of the same order such that A^(2)=I and...

    Text Solution

    |

  2. Let B is an invertible square matrix and B is the adjoint of matrix A ...

    Text Solution

    |

  3. First row of a matrix A is [1,3,2]. If adj A=[(-2,4,alpha),(-1,2,1),...

    Text Solution

    |

  4. Let A be a square matrix of order 3 satisfies the relation A^(3)-6A^(2...

    Text Solution

    |

  5. Which of the following matrices have eigen values as 1 and -1 ?

    Text Solution

    |

  6. Let A be a matrix of order 2xx2 such that A^(2)=O. A^(2)-(a+d)A+(ad-...

    Text Solution

    |

  7. Let A be a matrix of order 2xx2 such that A^(2)=O. tr (A) is equal t...

    Text Solution

    |

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

    Text Solution

    |

  9. If A and B are two square matrices of order 3xx3 which satify AB=A and...

    Text Solution

    |

  10. if A and B are two matrices of order 3xx3 so that AB=A and BA=B then (...

    Text Solution

    |

  11. If A and B are two square matrices of order 3xx3 which satify AB=A and...

    Text Solution

    |

  12. Consider an arbitarary 3xx3 non-singular matrix A[a("ij")]. A matrix B...

    Text Solution

    |

  13. Let A=[a("ij")] be 3xx3 matrix and B=[b("ij")] be 3xx3 matrix such tha...

    Text Solution

    |

  14. Let A=[(1,0,0),(1,0,1),(0,1,0)] satisfies A^(n)=A^(n-2)+A^(2)-I for n ...

    Text Solution

    |

  15. Let A=[(1,0,0),(1,0,1),(0,1,0)] satisfies A^(n)=A^(n-2)+A^(2)-I for n ...

    Text Solution

    |

  16. Let A=[(1,0,0),(1,0,1),(0,1,0)] satisfies A^(n)=A^(n-2)+A^(2)-I for n ...

    Text Solution

    |

  17. Let for A=[(1,0,0),(2,1,0),(3,2,1)], there be three row matrices R(1),...

    Text Solution

    |

  18. Let for A=[(1,0,0),(2,1,0),(3,2,1)], there be three row matrices R(1),...

    Text Solution

    |

  19. A and B are square matrices such that det. (A)=1, B B^(T)=I, det (B) g...

    Text Solution

    |

  20. A and B are square matrices such that det. (A)=1, B B^(T)=I, det (B) g...

    Text Solution

    |