Home
Class 12
MATHS
Let A be a 2xx2 matrix Statement -1 ad...

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

Text Solution

Verified by Experts

The correct Answer is:
B
`abs(adjA) = abs(A)^(n-1) = abs(A)^(2-1)=abs(A)`
`adj ("adj A")=abs(A)^(n-2)A`
`=abs(A)^(2-2) A= abs(A)^(0) A = A`
Promotional Banner

Similar Questions

Explore conceptually related problems

Statement-1 A is singular matrix of order nxxn, then adj A is singular. Statement -2 abs(adj A) = abs(A)^(n-1)

Let A be a 2 xx 2 matrix with non-zero entries and let A^2=I , where I is a 2 xx 2 identity matrix, Tr(A) = sum of diagonal elements of A, and |A| = determinant of matrix A. Statement 1: Tr(A)=0 Statement 2: |A| =1

Let A and B are symmetric matrices of order 3. Statement -1 A (BA) and (AB) A are symmetric matrices. Statement-2 AB is symmetric matrix, if matrix multiplication of A with B is commutative.

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, B, C are matrices such that abs(A_(3xx3))=3, abs(B_(3xx3))= -1 and abs(C_(2xx2)) = 2, abs(2 ABC) = - 12. Statement - 2 For matrices A, B, C of the same order abs(ABC) = abs(A) abs(B) abs(C).

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

P is a 2xx2 matrix . P'=P^(-1) then P=……..

Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A^2=""I . Statement 1: If A!=I and A!=""-I , then det A""=-1 . Statement 2: If A!=I and A!=""-I , then t r(A)!=0 . (1) Statement 1 is false, Statement ( 2) (3)-2( 4) is true (6) Statement 1 is true, Statement ( 7) (8)-2( 9) (10) is true, Statement ( 11) (12)-2( 13) is a correct explanation for Statement 1 (15) Statement 1 is true, Statement ( 16) (17)-2( 18) (19) is true; Statement ( 20) (21)-2( 22) is not a correct explanation for Statement 1. (24) Statement 1 is true, Statement ( 25) (26)-2( 27) is false.

Let F(x) be an indefinite integral of sin^(2)x Statement-1: The function F(x) satisfies F(x+pi)=F(x) for all real x. because Statement-2: sin^(2)(x+pi)=sin^(2)x for all real x. A) Statement-1: True , statement-2 is true,statement-2 is correct explanation for statement-1 (b) statement-1 true, statement-2 true and 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 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true Statement I: consider D= |a_1a_2a_3 b_1b_2b_3 c_1c_2c_3| let B_1, B_2,\ B_3 be the co-factors \ b_1, b_2, a n d\ b_3 respectively then a_1B_1+a_2B_2+a_3B_3=0 because Statement II: If any two rows (or columns) in a determinant are identical then value of determinant is zero a. A b. \ B c. \ C d. D

Statement I: If (log)_(((log)_5x))5=2,\ t h n\ x=5^(sqrt(5)) Statement II: (log)_x a=b ,\ if\ a >0,\ t h e n\ x=a^(1//b) 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;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false. Statement 1 is false, statement 2 is true