Home
Class 12
MATHS
Write a x2x matrix which is both symmetr...

Write a `x2x` matrix which is both symmetric and skew-symmetric.

Text Solution

Verified by Experts

For a symmetric matrix `A` with transpose `A^T`,
`A= A^T->(1)`
For a skew-symmetric matrix `A`,
`A= -A^T->(2)`
Adding (1) and (2),
`2A = 0`
`=>A = 0`
So, matrix `A` will have all elements as `0`.
...
Promotional Banner

Topper's Solved these Questions

  • CUET MOCK TEST 2022

    XII BOARDS PREVIOUS YEAR|Exercise Question|49 Videos

Similar Questions

Explore conceptually related problems

Write a 2xx2 matrix which is both symmetric and skew-symmetric.

If the matrix A is both symmetric and skew-symmetric , then

Write a matrix of order 3xx3 which is both symmetric and skew-symmetric matrix.

Write a square matrix of order 2, which is both symmetric and skew symmetric.

Write a square matrix which is both symmetric as well as skew-symmetric.

......... Matrix is both symmetric and skew-symmetric matrix.

A matrix which is both symmetric as well as skew-symmetric is a null matrix.

A matrix which is both symmetric as well as skew-symmetric is a null matrix.

Which of the following matrices is both symmetric and skew -symmetric ?

If the matrix A is both symmetric and skew symmetric,then (A) A is a diagonal matrix (B) A is a zero matrix (C) A is a square matrix (D) None of these

XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Write the principal value of cos^(-1)[cos(680^@)]

    Text Solution

    |

  2. Let R be the equivalence relation in the set A={0,\ 1,\ 2,\ 3,\ 4,\ 5}...

    Text Solution

    |

  3. Write a x2x matrix which is both symmetric and skew-symmetric.

    Text Solution

    |

  4. Write the projection of the vector 2 hat i- hat j+ hat k on the vector...

    Text Solution

    |

  5. int[x+3]/sqrt[5-4x-x^2].dx

    Text Solution

    |

  6. Evaluate : int0^(pi/2)x^2sinxdx

    Text Solution

    |

  7. If the three vectors veca, vecb , vecc are coplanar, prove that the ve...

    Text Solution

    |

  8. If vec a=2 hat i-3 hat j+ hat k , hat b=- hat i+ hat k , vec c=2 hat ...

    Text Solution

    |

  9. If y(x) is a solution of the differential equation ((2+sinx)/(1+y))...

    Text Solution

    |

  10. If x=a(cost+tsint)a n d y=a (sin t - t cos t), then find the value of ...

    Text Solution

    |

  11. If (x-y)dote^(x/(x-y))=a , Prove that y(dy)/(dx)+x=2ydot

    Text Solution

    |

  12. Using properties of determinants, prove the following : |[a, a^2,bc]...

    Text Solution

    |

  13. Write the value of the determinant |[p,p+1],[p-1,p]| .

    Text Solution

    |

  14. Let S be the set of all rational number except 1 and * be defined ...

    Text Solution

    |

  15. Find the distance of the point P(–1, –5, –10) from the point of int...

    Text Solution

    |

  16. Find the equation of the plane that contains the point (1, – 1, 2) ...

    Text Solution

    |

  17. A cottage industry manufactures pedestal lamps and wooden shades, e...

    Text Solution

    |

  18. Find the shortest distance between the lines l1 and l2 whose vector ...

    Text Solution

    |

  19. Find a unit vector perpendicular to both of the vectors vec a+ vec b ...

    Text Solution

    |

  20. Find a vector in the direction of vector 2 hat i-3 hat j+6 hat k k whi...

    Text Solution

    |