Home
Class 11
MATHS
Statement-1:Determination of a skew-symm...

Statement-1:Determination of a skew-symmetric matrix of order 3 is zero.
Statement-2: For any matrix `det(A)^(T)=det(A)=-det(A)`.
Where det(B) denotes the determinant of matrix B. Then:

A

Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 6

B

Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 6

C

Statement 1 is true, Statement 2 is False

D

Statement 1 is False, Statement 2 is true

Text Solution

Verified by Experts

The correct Answer is:
C
Let A be a skew - symmetric matrix of order 3
Then,
`A^(T) = -A`
`rArr Det (A^(T)) = Det (-A)`
`rArr Det (A) = (-1)^(3) Det (A)`
`rArr Det(A) = - Det(A)`
`rArr 2Det(A) = 0`
`rArr Det (A) = 0`
So, statement -1 is true.
For any square matrix of order n, we have
`Det(A^(T)) = Det(A) and Det(-A) = (-1)^(n) Det(A)`
So, statement -2 is not true
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|92 Videos

  • DETERMINANTS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • DETERMINANTS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|74 Videos

  • CARTESIAN CO-ORDINATE SYSTEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|27 Videos

  • DISCRETE PROBABILITY DISTRIBUTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|40 Videos

Similar Questions

Explore conceptually related problems

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,

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

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

If A and B are non - singular matrices of order 3xx3 , such that A=(adjB) and B=(adjA) , then det (A)+det(B) is equal to (where det(M) represents the determinant of matrix M and adj M represents the adjoint matrix of matrix M)

Statement-1 (Assertion and Statement- 2 (Reason) Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice as given below. Statement - 1 If A is skew-symnmetric matrix of order 3, then its determinant should be zero. Statement - 2 If A is square matrix, det (A) = det (A') = det (-A')

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?