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

If `P=[(1,alpha,3),(1,3,3),(2,4,4)]` is the adjoint of a 3 x 3 matrix A and `|A| = 4`, then `alpha` is equal to

A

11

B

5

C

0

D

4

Text Solution

Verified by Experts

The correct Answer is:
A
Given, adj A = P
`therefore abs("adj "A) = abs(P)`
` rArr abs(A)^(3-1) = abs(P) " "[because abs(A)=A]`
`rArr 16 = abs(P)`
`rArr 16 = abs((1,alpha,3),(1,3,3),(2,4,4))`
`rArr 16 = 1(0) - alpha (4-6) + 3(4-6) `
`rArr 16 = a alpha -6`
`rArr 2 alpha = 22`
`therefore alpha = 11`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|14 Videos

  • MATHEMATICAL INDUCTION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|31 Videos

Similar Questions

Explore conceptually related problems

If P=[[1, alpha, 3], [1, 3, 3], [2, 4, 4]] is the adjoint of 3times3 matrix A and |A|=4 , then alpha=

If P=[1alpha3 1 3 3 2 4 4] is the adjoint of a 3xx3 matrix A and |A|""=""4 , then a is equal to (1) 11 (2) 5 (3) 0 (4) 4

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

If A is 3xx3 matrix and |A|=4 , then |A^(-1)| is equal to

If M=[[1,c,3],[1,3,3],[2,4,4]] is the adjoint of a 3times3 matrix N and det(N)=4 ,then c is equal to

If P=[[1,alpha,31,3,32,4,4]] matrix A and ,|A|=4, then alpha is equal to

If P=[[1,alpha,31,3,32,4,4]] matrix A and ,|A|=4, then alpha is equal to

If A = {:[(2,-3),(4,1)]:} , then adjoint of matrix A is

ARIHANT MATHS-MATRICES -Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let M be a 3xx3 matrix satisfying M[0 1 0]=M[1-1 0]=[1 1-1],a n dM[1 1...

    Text Solution

    |

  2. Let A and B are symmetric matrices of order 3. Statement -1 A (BA) a...

    Text Solution

    |

  3. Let P = [a(ij)] " be a " 3 xx 3 matrix and let Q = [b(ij)], " where " ...

    Text Solution

    |

  4. If P is a 3xx3 matrix such that P^T = 2P+I, where P^T is the transpose...

    Text Solution

    |

  5. If the adjoint of a 3 3 matrix P is 1 4 4 2 1 7 1 1 3 , then the po...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. For 3xx3 matrices Ma n dN , which of the following statement (s) is (a...

    Text Solution

    |

  10. Let omega be a complex cube root of unity with omega!=1a n dP=[p(i j)]...

    Text Solution

    |

  11. If A is an 3xx3 non-singular matrix such that A A^T=A^TA and B=A^(-1)A...

    Text Solution

    |

  12. Let M be a 2xx2 symmetric matrix with integer entries. Then , M is i...

    Text Solution

    |

  13. Let m and N be two 3x3 matrices such that MN=NM. Further if M!=N^2 and...

    Text Solution

    |

  14. If A=[1 2 2 2 1-2a2b] is a matrix satisfying the equation AA^T=""9I , ...

    Text Solution

    |

  15. Let Xa n dY be two arbitrary, 3xx3 , non-zero, skew-symmetric matrices...

    Text Solution

    |

  16. If A=[5a-b3 2] and A adj A=AA^T , then 5a+b is equal to: (1) -1 (2) ...

    Text Solution

    |

  17. Let p=[(3,-1,-2),(2,0,alpha),(3,-5,0)], where alpha in RR. Suppose Q=[...

    Text Solution

    |

  18. let z= (-1+sqrt(3i))/2, where i=sqrt(-1) and r,s epsilon P1,2,3}. Let ...

    Text Solution

    |

  19. Let P=[[1,0,0],[4,1,0],[16,4,1]]and I be the identity matrix of order ...

    Text Solution

    |

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

    Text Solution

    |