Home
Class 12
MATHS
Let A, B, C, D be (not necessarily squar...

Let A, B, C, D be (not necessarily square) real matrices such that `A^T=BCD: B^T=CDA; C^T=DAB` and `D^T=ABC.` For the matrix `S=ABCD`, consider the two statements. I. `S^3=S` II. `S^2=S^4` (A) II is true but not I (B) I is true but not II (C) both I and II are true (D) both I and II are false

Text Solution

AI Generated Solution

To solve the problem, we need to analyze the given statements about the matrix \( S = ABCD \) and verify their validity based on the provided relationships between the matrices \( A, B, C, D \). ### Step-by-Step Solution: 1. **Understanding the Transpose Relationships**: We have the following relationships: - \( A^T = BCD \) - \( B^T = CDA \) ...
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE ENGLISH|Exercise CAE 13.1|5 Videos

  • MATRICES

    CENGAGE ENGLISH|Exercise CAE 13.2|6 Videos

  • MATRICES

    CENGAGE ENGLISH|Exercise Single correct Answer|34 Videos

  • MATHMETICAL REASONING

    CENGAGE ENGLISH|Exercise Archives|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|46 Videos

Similar Questions

Explore conceptually related problems

Let A, B, C, D be (not necessarily ) real matrices such that A^(T) = BCD , B^(T) =CDA, C^(T) = DAB and D^(T) =ABC for the matrix S = ABCD the least value of k such that S^(k) = S is

Let A,B,C,D be real matrices such that A^(T)=BCD,B^(T)=CDA,C^(T)=DAB and D^(T)=ABC for the matrix M=ABCD then find M^(3) ?

Let A and B be two square matrices satisfying A+BA^(T)=I and B+AB^(T)=I and O is null matrix then identity the correct statement.

Let A and B be two 2xx2 matrices. Consider the statements (i) A B=0 => A=0 or B=0 (ii) AB=I_2 => A=B^(-1) (a) only (i) (b) only (ii) (c) both are correct (d) none of these.

The area bounded by the two branches of curve (y-x)^2=x^3 and the straight line x=1 is (a) 1/5s qdotu n i t s (b) 3/5s qdotu n i t s 4/5s qdotu n i t s (d) 8/4s qdotu n i t s

In which phase of cell division are oogonia arrested (A) Anaphase II (B) Anaphase I (C) Interphase (D) Both A and B

Cyclic photophosphorylation is carried out by (a) P S I only (b) P S II only (c) Both a and b (d) Photolysis and P S II

For the following question, choose the correct answer from the codes (a), (b), (c) and (d) defined as follows: Statement I is true, Statement II is also true; Statement II is the correct explanation of Statement I. Statement I is true, Statement II is also true; Statement II is not the correct explanation of Statement I. Statement I is true; Statement II is false Statement I is false; Statement II is true. Let a , b , c , p , q be the real numbers. Suppose alpha,beta are the roots of the equation x^2+2p x+q=0 and alpha,1/beta are the roots of the equation a x^2+2b x+c=0, where beta^2 !in {-1,0,1}dot Statement I (p^2-q)(b^2-a c)geq0 and Statement II b !in p a or c !in q adot

The area of the loop of the curve a y^2=x^2(a-x) is 4a^2s qdotu n i t s (b) (8a^2)/(15)s qdotu n i t s (16 a^2)/9s qdotu n i t s (d) None of these

The area of the region of the plane bounded by max(|x|,|y|)lt=1 and x ylt=1/2 is (a) 1/2+ln2 s qdot u n i t s (b) 3+ln2 s qdot u n i t s (c) (31)/4 s qdot u n i t s (d) 1+2ln2 s qdot u n i t s

CENGAGE ENGLISH-MATRICES-ILLUSTRATION
  1. If a and B are square matrices of same order such that AB+BA=O, then p...

    Text Solution

    |

  2. Let A=[(1,2),(-1,3)] .If A^6=kA-205I then then numerical quantity of...

    Text Solution

    |

  3. Let A, B, C, D be (not necessarily square) real matrices such that A^T...

    Text Solution

    |

  4. If A and B are square matrices of the same order such that A B = B A,...

    Text Solution

    |

  5. If A=[-1 1 0-2] , then prove that A^2+3A+2I=Odot Hence, find Ba n dC m...

    Text Solution

    |

  6. If A=[(3,-4),(1,-1)] then find tr. (A^(2012)).

    Text Solution

    |

  7. If A is a nonsingular matrix satisfying AB-BA=A, then prove that det. ...

    Text Solution

    |

  8. If det, (A-B) ne 0, A^(4)=B^(4), C^(3) A=C^(3)B and B^(3)A=A^(3)B, the...

    Text Solution

    |

  9. Given a matrix A=[a b c b c a c a b],w h e r ea ,b ,c are real positiv...

    Text Solution

    |

  10. If M is a 3xx3 matrix, where det M=1a n dM M^T=1,w h e r eI is an iden...

    Text Solution

    |

  11. Consider point P(x, y) in first quadrant. Its reflection about x-axis ...

    Text Solution

    |

  12. If A=[[2,-2,-4],[-1,3,4],[1,-2,-3]] then A is 1) an idempotent matrix ...

    Text Solution

    |

  13. If A= [(1,1,3),(5,2,6),(-2,-1,-3)] then find A^(14)+3A-2I

    Text Solution

    |

  14. The matrix A=[-5-8 0 3 5 0 1 2-] is a. idempotent matrix b. involut...

    Text Solution

    |

  15. If abc=p and A=[(a,b,c),(c,a,b),(b,c,a)], prove that A is orthogonal i...

    Text Solution

    |

  16. Let A be an orthogonal matrix, and B is a matrix such that AB=BA, then...

    Text Solution

    |

  17. Find the adjoint of the matrix A=[(1,1,1),(2,1,-3),(-1,2,3)].

    Text Solution

    |

  18. If S=[((sqrt(3)-1)/(2sqrt(2)),(sqrt(3)+1)/(2sqrt(2))),(-((sqrt(3)+1)/(...

    Text Solution

    |

  19. If A is a square matrix such that A(adjA)=[(4,0,0),(0,4,0),(0,0,4)], t...

    Text Solution

    |

  20. Let A be a square matrix of order 3 such that adj. (adj. (adj. A)) =...

    Text Solution

    |