Home
Class 12
MATHS
If matrix A=[(0,1,-1),(4,-3,4),(3,-3,4)]...

If matrix `A=[(0,1,-1),(4,-3,4),(3,-3,4)]=B+C`, where B is symmetric matrix and C is skew-symmetric matrix, then find matrices B and C.

Text Solution

Verified by Experts

The correct Answer is:
`B=1/2 [(0,5,2),(5,-6,1),(2,1,8)], C=1/2[(0,-3,-4),(3,0,7),(4,-7,0)]`
Here matrix A is expressed as the sum of symmetric and skew-symmetric matrix. Then
`B=1/2(A+A^(T))` and `C=1/2 (A-A^(T))`
Now `A=[(0,1,-1),(4,-3,4),(3,-3,4)]`
`implies A^(T)=[(0,4,3),(1,-3,-3),(-1,4,4)]`
`implies B=1/2 ([(0,1,-1),(4,-3,4),(3,-3,4)]+[(0,4,3),(1,-3,-3),(-1,4,4)])`
`=1/2 [(0,5,2),(5,-6,1),(2,1,8)]`
and `C=1/2 ([(0,1,-1),(4,-3,4),(3,-3,4)]-[(0,4,3),(1,-3,-3),(-1,4,4)])`
`=1/2 [(0,-3,-4),(3,0,7),(4,-7,0)]`
Promotional Banner

Topper's Solved these Questions

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

Express the matrix A=[{:(-3,4,1),(2,3,0),(1,4,5):}] as the sum of symmetric matrix and a skew-symmetric matrix.

Express the matrix A={:[(4,2,-1),(3,5,7),(1,-2,1)]:} as the sum of a symmetric matrix and a skew-symmetric matrix.

Express the matrix B=[(2,-2,-4),(-1,3,4),(1,-2,-3)] as the sum of a symmetric and a skew symmetric matrix.

Express the marix A=|{:(3,2,3),(4,5,3),(2,4,5):}| as the sum of a symmetric matrix and a skew-symmetric matrix.

If Ais symmetric and B is skew-symmetric matrix, then which of the following is/are CORRECT ?

Express the matrix A={:[(-3,4,1),(2,3,0),(1,4,5)] as the sum of a symmetric and a skew. Symmetric matrix.

Show that the matrix A=[(0, 1,-1),(-1,0,1),(1,-1,0)] is a skew symmetric matrix.

Show that the matrix A=[(1, -1, 5),(-1,2,1),(5,1,3)] is a symmetric matrix.

Express the matric A= [[-3,4,1],[2,3,0],[1,4,5]] as the sum of a symmetric matrix and a skex symmetric matrix.

Express [[4,3,7],[6,5,-8],[1,2,6]] as the sum of a symmetric matrix and a skew symmetric matrix .

CENGAGE PUBLICATION-MATRICES-All Questions
  1. If A=[(1,2,3),(2,1,2),(2,2,3)]B=[(1,2,2),(-2,-1,-2),(2,2,3)] and C=[(-...

    Text Solution

    |

  2. If A=[(3,-2),(4,-1)], then find all the possible values of lambda such...

    Text Solution

    |

  3. If matrix A=[(0,1,-1),(4,-3,4),(3,-3,4)]=B+C, where B is symmetric mat...

    Text Solution

    |

  4. Consider the matrices A=[(4,6,-1),(3,0,2),(1,-2,5)], B=[(2,4),(0,1),...

    Text Solution

    |

  5. Let A=B B^(T)+C C^(T), where B=[(cos theta),(sin theta)], C=[(sin thet...

    Text Solution

    |

  6. if A=[[i,0] , [0,i]] where i=sqrt(-1) and x in N then A^(4x) equals to...

    Text Solution

    |

  7. If A = [[1,2],[3,-5]] and B=[[1,0],[0,2]] and X is a matrix such that ...

    Text Solution

    |

  8. Find the matrix X so that X[1 2 3 4 5 6]=[-7-8-9""""""2""""""4""""6]

    Text Solution

    |

  9. If A=[[costheta,sintheta],[-sintheta,costheta]],then Lim(ntooo)1/nA^n ...

    Text Solution

    |

  10. A=[(3,a,-1),(2,5,c),(b,8,2)] is symmetric and B=[(d,3,a),(b-a,e,-2b-c)...

    Text Solution

    |

  11. If A and B are matrices of the same order, then A B^T-B A^T is a (a)...

    Text Solution

    |

  12. If A and B are square matrices such that AB = BA then prove that A^(3)...

    Text Solution

    |

  13. If A is a square matrix such that A^(2)= I, then (A-I)^(3)+(A+I)^(3)...

    Text Solution

    |

  14. If B ,C are square matrices of order na n difA=B+C ,B C=C B ,C^2=O , t...

    Text Solution

    |

  15. Let A be any 3xx2 matrix. Then prove that det. (A A^(T))=0.

    Text Solution

    |

  16. Let A be a matrix of order 3, such that A^(T)A=I. Then find the value ...

    Text Solution

    |

  17. A and B are different matrices of order n satisfying A^(3)=B^(3) and A...

    Text Solution

    |

  18. Statement 1: if D=diag[d1, d2, ,dn],then D^(-1)=diag[d1^(-1),d2^(-1),...

    Text Solution

    |

  19. Point P(x, y) is rotated by an angle theta in anticlockwise direction....

    Text Solution

    |

  20. How many different diagonal matrices of order n can be formed which ar...

    Text Solution

    |