Home
Class 12
MATHS
For what value of x is the matrix A=[(0,...

For what value of `x` is the matrix `A=[(0,1,-2),(1,0,3),(x,3,0)]` a skew-symmetric matrix?

Text Solution

Verified by Experts

Given that,
`A=[(0,1,-2),(1,0,3),(x,3,0)]`
`A` is skew symmetric matrix
`A^T=[(0,1,x),(1,0,3),(-2,3,0)]`
`A^T=-A`
`[(0,1,x),(1,0,3),(-2,3,0)]=-[(0,1,-2),(1,0,3),(x,3,0)]`
Equating both sides,
`x=-(-2)=2`

...
Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA|Exercise QUESTION|1 Videos
  • ALGEBRA OF VECTORS

    RD SHARMA|Exercise Solved Examples And Exercises|331 Videos

Similar Questions

Explore conceptually related problems

For what value of x, is the matrix A=[(0,1,-2),(-1,x,-3),(2,3,0)] a skew-symmetric matrix

For what value of x is the matrix A=[[0,1,-21,0,3x,3,0]] a skew-symmetric matrix?

The value of 'x', when the matrix : A=[(0,1,-2),(-1,0,3),(x,-3,0)] is a skew - symmetric matrix is _____________.

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

Prove that A=[(0,1,2),(-1,0,3),(-2,-3,0)] is a skew symmetric matrix as A^T =-A .

(i) Show that the matrix A=[(1,-1,5),(-1,2,1),(5,1,3)] is a symmetric matrix. Show that the matrix A=[(0,1,-1),(-1,0,1),(1,-1,0)] is a skew symmetric matrix

Consider the following statements in respect of the matrix A=[{:(0,1,2),(-1,0,-3),(-2,3,0):}] 1. The matrix A is skew-symmetric. 2. The matrix A is symmetric. 3. The matrix A is invertible. Which of the above statements is/are correct ?

Consider the following statements in respect of the matrix A=[{:(0,1,2),(-1,0,-3),(-2,3,0):}] I. The matrix A is skew symmetric II. The matrix A is symmetric III. The matrix A is invertible Which of the above statements is/are correct ?

Is the matrix A=[[0,-1,2],[1,0,-3],[-2,3,0]]. symmetric or skew symmetric? Give reasons

[{:(2,0,0),(3,-1,0),(-7,3,1):}] is a skew symmetric matrix. True or False.

RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If [[9,-1, 4],[-2, 1, 3]]=A+[[1 ,2,-1],[ 0, 4, 9]] , then find matrix ...

    Text Solution

    |

  2. If [(a-b,2a+c),(2a-b,3c+d)]=[(-1, 5),( 0, 13)] , find the value of b

    Text Solution

    |

  3. For what value of x is the matrix A=[(0,1,-2),(1,0,3),(x,3,0)] a skew-...

    Text Solution

    |

  4. If matrix A=[[2,-2],[-2, 2]] and A^2=p A , then write the value of p

    Text Solution

    |

  5. If A is a square matrix such that A^2=A , then write the value of 7A-(...

    Text Solution

    |

  6. If 2[[3, 4, 5x]]+[[1y,0, 1]]=[[7 0, 10, 5]] , find x-y .

    Text Solution

    |

  7. If [[x,1]][(1 ,0),(-2, 0)]=O , find x

    Text Solution

    |

  8. If [a+4 3b8-6]=[2a+2b+2 8a-8b] , write the value of a-2b .

    Text Solution

    |

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

    Text Solution

    |

  10. If [(x y,4),(z+6,x+y)]=[(8,w),(0, 6)] , write the value of (x+y+z) .

    Text Solution

    |

  11. Construct a 2xx2 matrix A=[a(i j)] whose elements a(i j) are given by ...

    Text Solution

    |

  12. If [x+y x-y]=[2 1 4 3][1-2] , then write the value of (x ,\ y) .

    Text Solution

    |

  13. Matrix A=[0 2b-2 3 1 3 3a3-1] is given to be symmetric, find the value...

    Text Solution

    |

  14. Write the number of all possible matrices of order 2xx2 with each e...

    Text Solution

    |

  15. If [2\ \ 1\ \ 3][-1 0-1-1 1 0 0 1 1][1 0-1]=A , then write the order o...

    Text Solution

    |

  16. If A=[3 5 7 9] is written as A=P+Q , where P is symmetric and Q is sk...

    Text Solution

    |

  17. If A=[(1 ,0, 0),(0, 1,0),( a,b, -1)] , then A^2 is equal to (a) a n...

    Text Solution

    |

  18. If A=[i0 0i],\ n in N , then A^(4n) equals [0i i0] (b) [0 0 0 0] (c) ...

    Text Solution

    |

  19. If A and B are two matrices such that A B=A and B A=B , then B^...

    Text Solution

    |

  20. If A B=A and B A=B , where A and B are square matrices, then B^2=B ...

    Text Solution

    |