Home
Class 12
MATHS
Let A be a 2xx2 matrix with non-zero en...

Let A be a `2xx2` matrix with non-zero entries and let `A^2=""I` , where I is `2xx2` identity matrix. Define Tr(A) = sum of diagonal elements of A and |A| = determinant of matrix A. Statement-1: `T r(A)""=""0` Statement-2: `|A|""=""1` (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

A

Statement (1) is true and statement (2) is true and statement (2) is correct explanation for Statement (1)

B

Statement (1) is true and statement (2) is true and statement (2) is NOT a correct explanation for Statement (1)

C

Statement (1) is true but (2) is false

D

Statement (1) is false but (2) is true

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MOTION|Exercise Exercise - 4 (Level-II)|28 Videos

  • MATRICES

    MOTION|Exercise Exercise - 3(Matrix Match - type Questions)|1 Videos

  • LIMIT

    MOTION|Exercise EXERCISE-4|17 Videos

  • MAXIMA AND MINIMA

    MOTION|Exercise EXERCISE - 4 (LEVEL - II)|17 Videos

Similar Questions

Explore conceptually related problems

Let A be a 2xx2 matrix with non zero entries and let A^(2)=I , where I is 2xx2 identity matrix. Define Tr(A)= sum of diagonal elemets of A and |A|= determinant of matrix A. Statement 1: Tr(A)=0 Statement 2: |A|=1 .

Let A be a 2xx2 matrix with non-zero entries and let A^(^^)2=I, where i is a 2xx2 identity matrix,Tr(A)i=sum of diagonal elements of A and |A|= determinant of matrix A.Statement 1:Tr(A)=0 Statement 2:|A|=1

Let f: R R be a continuous function defined by f(x)""=1/(e^x+2e^(-x)) . Statement-1: f(c)""=1/3, for some c in R . Statement-2: 0""<""f(x)lt=1/(2sqrt(2)), for all x in R . (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Let S_1=sum_(j=1)^(10)j(j-1)^(10)C_j ,""S_2=sum_(j=1)^(10)j""^(10)C_i("andS")_"3"=sum_(j=1)^(10)j^2""^("10")"C"_"j"dot Statement-1: S_3=""55xx2^9 Statement-2: S_1=""90xx2^8a n d""S_2=""10xx2^8 . (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Statement-1: The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane x""""y""+""z""=""5 . Statement-2: The plane x x""""y""+""z""=""5 bisects the line segment joining A(3, 1, 6) and B(1, 3, 4). (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Let A be a 2""xx""2 matrix Statement 1 : a d j""(a d j""A)""=""A Statement 2 : |a d j""A|""=""|A| (1) Statement1 is true, Statement2 is true, Statement2 is a correct explanation for statement1 (2) Statement1 is true, Statement2 is true; Statement2 is not a correct explanation for statement1. (3) Statement1 is true, statement2 is false. (4) Statement1 is false, Statement2 is true

Statement-1: intsin^-1xdx+intsin^-1sqrt(1-x^2)dx=pi/2x+c Statement-2: sin^-1x+cos^-1x=pi/2 (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.

If A is 2 x 2 invertible matrix such that A=adjA-A^-1 Statement-I 2A^2+I=O(null matrix) Statement-II: 2|A|=1 (i) Statement-I is true, Statement-II is true; Statement-II is a correct explanation for Statement-I (2) Statement-I is true, Statement-II is true; Statement-II is not a correct explanation for Statement-I. 3) Statement-I is true, Statement-II is false. (4) Statement-I is false, Statement-II is true.

Statement-1: The function F(x)=intsin^2xdx satisfies F(x+pi)=F(x),AAxinR ,Statement-2: sin^2(x+pi)=sin^2x (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.

Statement-1: int((x^2+1)/x^2)e^((x^2+1)/x^(2))dx=e^((x^2+1)/x^(2))+C Statement-2: intf(x)e^(f(x))dx=f(x)+C (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.

MOTION-MATRICES -Exercise - 4 (Level-I)
  1. If A^2-A +I = 0, then the inverse of A is: (A) A+I (B) A (C) ...

    Text Solution

    |

  2. If A=[(1,0),(1,1)] and I=[(1,0),(0,1)] , then which one of the fo...

    Text Solution

    |

  3. If A and B are square matrices of order n xx n such that A^2-B^2=(A-B)...

    Text Solution

    |

  4. Let {:A=[(1,2),(3,4)]and BA=[(a,0),(0,b)]:},a,b in N Then,

    Text Solution

    |

  5. Let A=[5 5alphaalpha0alpha5alpha0 0 5]dot"I f"|A^2|=25 , then |alpha| ...

    Text Solution

    |

  6. Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identi...

    Text Solution

    |

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

    Text Solution

    |

  8. The number of 3 3 non-singular matrices, with four entries as 1 and ...

    Text Solution

    |

  9. Let A be a 2xx2 matrix with non-zero entries and let A^2=""I , whe...

    Text Solution

    |

  10. If omega !=1 is the complex cube root of unity and matrix H=[(omega,...

    Text Solution

    |

  11. Let A and B be two symmetric matrices of order 3. Statement-1 : A(BA) ...

    Text Solution

    |

  12. Let omega!=1 be cube root of unity and S be the set of all non-singula...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. If A is a 3 xx 3 non-singular matrix such that A A^(T) = A^(T)A " and ...

    Text Solution

    |

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

    Text Solution

    |

  18. If A=|{:(,5a,-b),(,3,2):}| and A adj A=A A^(T), then 5a+b is equal to

    Text Solution

    |

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

    Text Solution

    |