Home
Class 12
MATHS
If a square matix a of order three is de...

If a square matix a of order three is defined `A=[a_("ij")]` where `a_("ij")=s g n(i-j)`, then prove that A is skew-symmetric matrix.

Text Solution

Verified by Experts

We know that
`sgn(x)={("1, if "x gt 0),(-"1, if "xlt0),("0, if "x=0):}`
`:. a_("ij")=sgn (i-j)={("1, if "igt j),(-"1, if "i ltj),("0, if "i=j):}`.
`:. A=[(0,-1,-1),(1,0,-1),(1,1,0)]`
Hence, matrix A is skew-symmetric.
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise Exercise 13.1|5 Videos

  • MATRICES

    CENGAGE|Exercise Exercise 13.2|6 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Single Correct Answer Type|46 Videos

Similar Questions

Explore conceptually related problems

If A=|a_(ij)]_(2 xx 2) where a_(ij) = i-j then A =………….

If a square matrix A=[a_(ij)]_(3 times 3) where a_(ij)=i^(2)-j^(2) , then |A|=

If A=[a_(ij)] is a square matrix of even order such that a_(ij)=i^(2)-j^(2), then A is a skew- symmetric matrix and |A|=0 (b) A is symmetric matrix and |A| is a square (c) A is symmetric matrix and |A|=0 (d) none of these

Statement-1 (Assertion and Statement- 2 (Reason) Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice as given below. Statement - 1 A=[a_(ij)] be a matrix of order 3xx3 where a_(ij) = (i-j)/(i+2j) cannot be expressed as a sum of symmetric and skew-symmetric matrix. Statement-2 Matrix A= [a_(ij)] _(nxxn),a_(ij) = (i-j)/(i+2j) is neither symmetric nor skew-symmetric.

If A=[a_(ij)] is a square matrix such that a_(ij)=i^(2)-j^(2), then write whether A is symmetric or skew-symmetric.

"In a square matrix "A=a_(ij)" if i>j then "a_(ij)=0" then the Matrix A is"

The square matrix A=[a_(ij)" given by "a_(ij)=(i-j)^3 , is a

the square matrix A=[a_(ij)]_mxxm given by a_(ij)=(i-j)^(n), show that A is symmetic and skew-sysmmetic matrices according as n is even or odd, repectively.

Statement 1: The determinant of a matrix A=[a_(ij)]_(5xx5) where a_(ij)+a_(ji)=0 for all i and j is zero.Statement 2: The determinant of a skew-symmetric matrix of odd order is zero

CENGAGE-MATRICES-Solved Examples And Exercises
  1. If a square matix a of order three is defined A=[a("ij")] where a("ij"...

    Text Solution

    |

  2. In which of the following type of matrix inverse does not exist always...

    Text Solution

    |

  3. If both A-1/2Ia n dA+1/2 are orthogonal matices, then (a)A is ortho...

    Text Solution

    |

  4. If nth-order square matrix A is a orthogonal, then |adj(adjA)| is (...

    Text Solution

    |

  5. If P is an orthogonal matrix and Q=P A P^T an dx=P^T Q^1000 P then x^...

    Text Solution

    |

  6. If A is a nilpotent matrix of index 2, then for any positive integer n...

    Text Solution

    |

  7. If Aa n dB are two matrices such that A B=Ba n dB A=A ,t h e n (A^5-B...

    Text Solution

    |

  8. If Z is an idempotent matrix, then (I+Z)^n I+2^n Z b. I+(2^n-1)Z c. ...

    Text Solution

    |

  9. If A is an orthogonal matrix then A^(-1) equals A^T b. A c. A^2 d. non...

    Text Solution

    |

  10. If A^2=1, then the value of det(A-I) is (where A has order 3) 1 b. -1 ...

    Text Solution

    |

  11. Let A be an nth-order square matrix and B be its adjoint, then |A B+K ...

    Text Solution

    |

  12. A=[(a,1,0),(1,b,d),(1,b,c)],B=[(a,1,1),(0,d,c),(f,g,h)],U=[(f),(g),(h)...

    Text Solution

    |

  13. If M is a 3 xx 3 matrix, where det M=1 and MM^T=1, where I is an ident...

    Text Solution

    |

  14. If A is a diagonal matrix of order 3xx3 is commutative with every squa...

    Text Solution

    |

  15. Let S be the set which contains all possible vaues fo I ,m ,n ,p ,q ,r...

    Text Solution

    |

  16. 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

    |

  17. If A is a square matrix of order 3 such that |A|=2,t h e n|(a d jA^(-1...

    Text Solution

    |

  18. Let A=[[3x^2], [1], [6x]],B=[a,b,c]and C=[[(x+2)^2, 5x^2, 2x],[5x^2, 2...

    Text Solution

    |

  19. If A is an idempotent matrix satisfying, (I-0. 4 A)^(-1)=I-alphaA ,w h...

    Text Solution

    |

  20. Let A=([a(i j)])(3xx3) be a matrix such that AA^T=4Ia n da(i j)+2c(i j...

    Text Solution

    |

  21. Let A be the set of all 3xx3 skew-symmetri matrices whose entries are ...

    Text Solution

    |