Home
Class 12
MATHS
Let Ad nB be 3xx3 matrtices of ral numbe...

Let `Ad nB` be `3xx3` matrtices of ral numbers, where `A` is symmetric, `"B"` is skew-symmetric , and `(A+B)(A-B)=(A-B)(A+B)dot` If `(A B)^t=(-1)^k A B ,w h e r e(A B)^t` is the transpose of the mattix `A B ,` then find the possible values of `kdot`

A

any integer

B

odd integer

C

even integer

D

cannot say anything

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    DISHA PUBLICATION|Exercise Exercise 1: Concept Builder (Topic 3)|23 Videos

  • MATHEMATICAL REASONING

    DISHA PUBLICATION|Exercise Exercise-2 : Concept Applicator|30 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    DISHA PUBLICATION|Exercise Exercise-2 Concept Applicator|20 Videos

Similar Questions

Explore conceptually related problems

Let A dn B be 3xx3 matrtices of ral numbers,where A is symmetric,B is skew- symmetric,and (A+B)(A-B)=(A-B)(A+B). If (AB)^(t)=(-1)^(k)AB, where (AB)^(t) is the transpose of the mattix AB, then find the possible values of k.

Let A and B are 3xx3 matrices with real number entries, where A is symmetric, B is skew - symmetric and (A+B)(A-B)=(A-B)(A+B) . If (AB)^(T)=(-1)^(k)AB , then the sum of all possible integral value of k in [2, 10] is equal to (where A^(T) represent transpose of matrix A)

If A is skew-symmetric and B=(I-A)^(-1)(I+A), then B is

Let A and B be any two 3xx3 matrices . If A is symmetric and B is skew -symmetric then the matrix AB-BA is :

If A is a symmetric and B skew symmetric matrix and (A+B) is non-singular and C=(A+B)^(-1)(A-B), then prove that

If A is symmetric and B skew- symmetric matrix and A + B is non-singular and C= (A+B) ^(-1) (A-B) , C^(T)(A+B)C equals to

If A is symmetric and B skew- symmetric matrix and A + B is non-singular and C= (A+B) ^(-1) (A-B) C^(T) AC equals to

Let A and B be symmetric matrices of same order. Then A+B is a symmetric matrix, AB-BA is a skew symmetric matrix and AB+BA is a symmetric matrix

DISHA PUBLICATION-MATRICES-Exercise 2: Concept Applicator
  1. Let A,B and C be nxxn matrices. Which one of the following is a correc...

    Text Solution

    |

  2. If A=1/pi[sin^(-1)(pix)tan^(-1)(x/pi)sin^(-1)(x/pi)cot^(-1)(pix)] and ...

    Text Solution

    |

  3. Let Ad nB be 3xx3 matrtices of ral numbers, where A is symmetric, "B" ...

    Text Solution

    |

  4. If P=[[sqrt3/2,1/2] , [-1/2,sqrt3/2]] and A=[[1,1] , [0,1]] and Q=PAP^...

    Text Solution

    |

  5. If [(0,2b,c),(a,b,-c),(a,-b,c)] is orthogonal matrix, then the value ...

    Text Solution

    |

  6. If A is a square matrix of order m, then the matrix B of same order is...

    Text Solution

    |

  7. If A1, A2, , A(2n-1)a r en skew-symmetric matrices of same order, the...

    Text Solution

    |

  8. For k=1/sqrt(50), the value of a, b, c such that PP' = I, where P=[(2/...

    Text Solution

    |

  9. IfA^(k)= 0 (Ais nilpotent with index k), (I-A)^(p)=I+A+A^(2)+. . .+A^(...

    Text Solution

    |

  10. If A and B are two square matrices such that B=-A^(-1)BA, then (A+B)^(...

    Text Solution

    |

  11. If A=[(1,-1),(2,-1)] and B=[(1,a),(4,b)] and (A+B)^(2)=A^(2)+B^(2). ...

    Text Solution

    |

  12. If A is a square matrix such that A A^T=I=A^TA, then A is

    Text Solution

    |

  13. If Aa n dB are symmetric matrices of the same order and X=A B+B Aa n d...

    Text Solution

    |

  14. [{:(2x+y,4x),(5x-7,4x):}]=[{:(7,7y-13),(y,x+6):}] then the value of x,...

    Text Solution

    |

  15. Given that [(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,omega...

    Text Solution

    |

  16. If {:A=[(alpha,0),(1,1)]andB=[(1,0),(5,1)]:}, then te value of alpha f...

    Text Solution

    |

  17. [[i,0,0],[0,i,0],[0,0,i]] then A^(4n+1) =.... n in N

    Text Solution

    |

  18. The matrix A=[0-5 8 5 0 12-8-12 0] is a (a) diagonal matrix (b) symmet...

    Text Solution

    |

  19. If A=[(alpha,0),(1,1)] and B=[(9,a),(b,c)] and A^(2)=B, then the value...

    Text Solution

    |

  20. Find the value of k so that A^2=8A+kI where A=[(1,0),(-1,7)].

    Text Solution

    |