Home
Class 12
MATHS
If P=[(1,alpha,3),(1,3,3),(2,4,4)] is th...

If `P=[(1,alpha,3),(1,3,3),(2,4,4)]` is the adjoint of a `3xx3` matrix A and det. `(A)=4`, then the value of alpha is ______ .

Text Solution

Verified by Experts

The correct Answer is:
11
A= adj. B
`implies |A|=|"adj. B"|=|B|^(2)`
`:. |A|=(4)^(2) implies |A|=16`
`implies |(1,x,3),(1,3,3),(2,4,4)|=16`
`implies 1(0)-x(-2)+3(-2)=16`
`implies 2x=22`
`implies x=11`
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

Let A be a 2xx3 matrix, whereas B be a 3xx2 amtrix. If det.(AB)=4 , then the value of det.(BA) is

Roots of the equation 3x^2 -6x+4=0 are alpha and beta then find the value of alpha^3 +beta^3

If A=[{:(3,-3,4),(2,-3,4),(0,-1,1):}] , then the trace of the matrix Adj(AdjA) is

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

If P={:[(2,-2,-4),(-1,3,4),(1,-2,-3)]:} then show that, p^(2)=p .

If x+4y=14 is a normal to the curve y^2=ax^3 -beta at (2,3) then value of alpha+beta is

[(7,1,2),(9,2,1)]xx[(3),(4),(5)]+2[(4),(2)] is equal to the matrix-

tan (alpha + beta) =1/2, tan(alpha - beta) = 1/3 "then the value of" tan^(2) alpha is-

IF alpha and beta are the roots of the equation x(x-3)=4, find the value of alpha^2+beta^2 .

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

CENGAGE PUBLICATION-MATRICES-All Questions
  1. Let A and B are two square matrices of order 3 such that det. (A)=3 an...

    Text Solution

    |

  2. Let P, Q and R be invertible matrices of order 3 such A=PQ^(-1), B=QR^...

    Text Solution

    |

  3. If P=[(1,alpha,3),(1,3,3),(2,4,4)] is the adjoint of a 3xx3 matrix A a...

    Text Solution

    |

  4. A, B and C are three square matrices of order 3 such that A= diag (x, ...

    Text Solution

    |

  5. Let A=[a("ij")] be a matrix of order 2 where a("ij") in {-1, 0, 1} and...

    Text Solution

    |

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

    Text Solution

    |

  7. The number of 3 x 3 non-singular matrices, with four entries as 1 and ...

    Text Solution

    |

  8. Let A be a 2 xx 2 matrix with non-zero entries and let A^2=I, where i ...

    Text Solution

    |

  9. Let A and B two symmetric matrices of order 3. Statement 1 : A(BA) a...

    Text Solution

    |

  10. Let A=((1,0,0),(2,1,0),(3,2,1)). If u(1) and u(2) are column matrices ...

    Text Solution

    |

  11. Let P and Q be 3xx3 matrices with P!=Q . If P^3=""Q^3a n d""P^2Q""=""Q...

    Text Solution

    |

  12. If P=[(1,alpha,3),(1,3,3),(2,4,4)] is the adjoint of a 3xx3 matrix A a...

    Text Solution

    |

  13. If A is an 3xx3 non-singular matrix such that A A^T=A^T A and B""=""...

    Text Solution

    |

  14. If A=[(5a,-b),(3, 2)] and A adj A=A A^T , then 5a+b is equal to: (1) ...

    Text Solution

    |

  15. if A=[[2,-3],[-4,1]] then (3A^2+12A)=?

    Text Solution

    |

  16. The number of 3xx3 matrices A whose entries are either 0or1 and for wh...

    Text Solution

    |

  17. Let omega != 1 be cube root of unity and S be the set of all non-sing...

    Text Solution

    |

  18. Let P=[a(i j)] be a 3xx3 matrix and let Q=[b(i j)],w h e r eb(i j)=2^(...

    Text Solution

    |

  19. Let P=[(1,0,0),(3,1,0),(9,3,1)] and Q = [q(ij)] be two 3xx3 matrices s...

    Text Solution

    |

  20. How many 3xx3 matrices M with entries from {0,1,2} are there, for whic...

    Text Solution

    |