Home
Class 12
MATHS
Statement-1 (Assertion and Statement- 2 ...

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')`

A

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

B

Statement-1 is true, Statement-2 is true, Sttatement - 2
is not a correct explanation for Stamtement-1

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
Statement -2 is false
`because det (A^(-1)) ne det (-A')`
`[because det (-A')=(-1)^(3) det (A') = - det(A') ]`
but in Statement-1
`A'=-A rArr A = -A'`
`therefore det(A) = det(-A')`
`=- det A' = - det (A)`
`rArr 2 det (A) = 0`
` therefore det (A) = 0`
Then, Statement - 1 is true.
Promotional Banner

Topper's Solved these Questions

  • MATRICES

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

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Matrices Exercise 5 : (Matching Type Questions )|4 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

Assertion (A): If A is skew symmetric matrix of order 3 then its determinant should be zero Reason (R): If A is square matrix then det(A)=det(A')=det(A')

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 For a singular matrix A , if AB = AC rArr B = C Statement-2 If abs(A) = 0, thhen A^(-1) does not exist.

Statement -1 (Assertion) and Statement - 2 (Reason) Each of these examples 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 A is singular matrox pf order nxxn, then adj A is singular. Statement -2 abs(adj A) = abs(A)^(n-1)

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 Let A 2xx2 matrix A has determinant 2. If B= 9 A^(2) , the determinant of B^(T) is equal to 36. Statement- 2 If A, B and C are three square matrices Such that C= AB then abs(C) = abs(A) abs(B).

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 and B are two square matrices of order nxxn which satisfy AB= A and BA = B, then (A+B) ^(7) = 2^(6) (A+B) Statement- 2 A and B are unit matrices.

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 A=[a_(ij)] be a matrix of order 3xx3 where a_(ij) = (i-j)/(i+2j) cannot be expressed as a sum of symmetric and skew-symmetric matrix. Statement-2 Matrix A= [a_(ij)] _(nxxn),a_(ij) = (i-j)/(i+2j) is neither symmetric nor skew-symmetric.

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 The determinant fo a matrix A= [a_(ij)] _(nxxn), where a_(ij) + a_(ji) = 0 for all i and j is zero. Statement- 2 The determinant of a skew-symmetric matrix of odd order is zero.

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. Let A be a skew-symmetric matrix, B= (I-A) (I+A)^(-1) and X and Y be column vectors conformable for multiplication with B. Statement-1 (BX)^(T) (BY) = X^(T) Y Statement- 2 If A is skew-symmetric, then (I+A) is non-singular.

Statement-1(Assertion) and Statement-2 (reason) Each of these question also has four alternative choices, only one of which is the correct answer. You have to select the correct choice as given below. (a) Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1 Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement -1 (c) Statement -1 is true, Statement -2 is false (d) Statement -1 is false, Statement -2 is true Statement -1 log_x3.log_(x//9)3=log_81(3) has a solution. Statement-2 Change of base in logarithms is possible .