Home
Class 12
MATHS
Statement -1 : Determinant of a skew-sym...

Statement -1 : Determinant of a skew-symmetric matrix of order 3 is zero.
Statement -2 : For any matrix A, Det `(A) = "Det"(A^(T)) and "Det" (-A) = - "Det" (A)`
where Det (B) denotes the determinant of matrix B. Then,

A

Both statement are true

B

Both statement ar false

C

Statement-1 is false and statement-2 is true

D

Statement-1 is true and statement-2 is false

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MATRICES & DETERMINANT

    RESONANCE ENGLISH|Exercise HLP|34 Videos

  • MATRICES & DETERMINANT

    RESONANCE ENGLISH|Exercise EXERCISE-3|31 Videos

  • INDEFINITE INTEGRATION

    RESONANCE ENGLISH|Exercise SELF PRACTIC PROBLEMS|25 Videos

  • NUMBER THEORY

    RESONANCE ENGLISH|Exercise Exercise -2 (PART - II)|4 Videos

Similar Questions

Explore conceptually related problems

If A is a skew-symmetric matrix of order 3, then prove that det A = 0 .

Assertion: Determinant of a skew symmetric matrix of order 3 is zero. Reason: For any matix A, det(A^T)=det(A) and det(-S)=-det(S) (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true and R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

If matric A is skew-symmetric matric of odd order, then show that tr. A = det. A.

If A is a matrix of order 3, then det(kA) is

If one of the eigenvalues of a square matrix a order 3xx3 is zero, then prove that det A=0 .

The inverse of a skew-symmetric matrix of odd order a. is a symmetric matrix b. is a skew-symmetric c. is a diagonal matrix d. does not exist

If A is a skew symmetric matrix of order 3 , B is a 3xx1 column matrix and C=B^(T)AB , then which of the following is false?

If A is an invertible matrix of order 2, then det (A^(-1)) is equal to (A) det (A) (B) 1/(det(A) (C) 1 (D) 0

If B is a skew-symmetric matrix, write whether the matrix A BA^T is symmetric or skew-symmetric.

If A is skew symmetric matrix, then I - A is (where I is identity matrix of the order equal to that of A)

RESONANCE ENGLISH-MATRICES & DETERMINANT-PART-II:
  1. If omega^3=1 is the complex cube root of unity and matrix H=|{:(,omega...

    Text Solution

    |

  2. If the trivial solution is the only solution of the system of equation...

    Text Solution

    |

  3. Statement -1 : Determinant of a skew-symmetric matrix of order 3 is ze...

    Text Solution

    |

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

    Text Solution

    |

  5. Let P and Q be 3xx3 matrices P ne Q. If P^(3)=Q^(3) and P^(2)Q=Q^(2)P,...

    Text Solution

    |

  6. The number of values of k for which the system of equations (k+1)x+8y=...

    Text Solution

    |

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

    Text Solution

    |

  8. if alpha, beta , ne 0 " and " f(n) =alpha^(n)+beta^(n) " and " |{:(...

    Text Solution

    |

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

    Text Solution

    |

  10. If A=[(1,2,2),(2,1,-2),(a,2,b)] is a matrix satisying the equation A A...

    Text Solution

    |

  11. The set of all values of lambda for which the system of linear equ...

    Text Solution

    |

  12. The system of linear equations x+lambday-z=0, lambdax-y-z=0, x+y-lam...

    Text Solution

    |

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

    Text Solution

    |

  14. If S is the set of distinct values of 'b' for which the following ...

    Text Solution

    |

  15. If A=|{:(,2,-3),(,-4,1):}| then adj (3A^(2)+12A) is equal to

    Text Solution

    |

  16. If the system of linear equations. x+ky+3z=0 3x+ky-2z=0 2x+4y...

    Text Solution

    |

  17. if |{:(x-4,,2x,,3x),(2x,,x-4,,2x),(2x,,2x,,x-4):}|=(A+Bx)(x-A)^(2), th...

    Text Solution

    |

  18. The system of linear equations x + y + z = 2 2x + 3y + 2z = 5 2...

    Text Solution

    |

  19. If A = [(costheta,-sintheta),(sintheta,costheta)], then the matrix A^(...

    Text Solution

    |

  20. Let d in R, and A[{:(,-2,4+d,(sin theta-2)),(,1,(sin theta)+2,d),(,5,(...

    Text Solution

    |