Home
Class 12
MATHS
Show that BAB' is symmetric or skw-symme...

Show that BAB' is symmetric or skw-symmetirc according as A is symmetric or skw-symmetric (where B is any square matrix whose order is same as that of A).

Text Solution

Verified by Experts

CASE=A os symmetric
`(BAB')'=(B')'A'B'=BAB Rightarrow BAB'"is symmetric"`
CASE-II A is skew-symmetric `Rightarrow A'=-A`
(BAB)'=(B')' A'B'
`=b(-A)B'`
`=-(BAB')`
`Rightarrow` BAB' is skew-symmetric
Promotional Banner

Topper's Solved these Questions

  • MATRICES & DETERMINANT

    RESONANCE|Exercise EXERCISE-1|7 Videos

  • MATRICES & DETERMINANT

    RESONANCE|Exercise SECTION-B|18 Videos

  • INDEFINITE INTEGRATION

    RESONANCE|Exercise SELF PRACTIC PROBLEMS|25 Videos

  • NUMBER THEORY

    RESONANCE|Exercise Exercise -2 (PART - II)|4 Videos

Similar Questions

Explore conceptually related problems

Show that the matrix B^(T)AB is symmetric or skew-symmetric according as A is symmetric or skew-symmetric.

Show that the matrix B^(T)AB is symmetric or skew-symmetric according as A is symmetric or skew-symmetric.

Show that the matrix B^(^^), AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.

If A is a square matrix, then A is skew symmetric if

if B is skew symmetric matrix then find matrix ABA^(T) is symmetric or skew symmetric

If B is a symmetric matrix,write whether the matrix ABA^(T) is symmetric or skew- symmetric.

If A is symmetric, show that B' AB is symmetric.

For any square matrix write whether AA^(T) is symmetric or skew-symmetric.

If A is any square matrix,then A+A^(T) is skew symmetric

If A is skew symmetric matrix, then I - A is (where I is identity matrix of the order equal to that of A)

RESONANCE-MATRICES & DETERMINANT-HLP
  1. Show that BAB' is symmetric or skw-symmetirc according as A is symmetr...

    Text Solution

    |

  2. If a^2+b^2+c^2=1, then prove that |a^2+(b^2+c^2)cosvarphia b(1-cosv...

    Text Solution

    |

  3. prove that |{:((a-x)^(2),,(a-y)^(2),,(a-z)^(2)),((b-x)^(2),,(b-y)^(2),...

    Text Solution

    |

  4. Prove that Delta=|{:(,beta(gamma),beta(gamma)'+beta'(gamma),beta'(gamm...

    Text Solution

    |

  5. If a x1 2+b y1 2+c z1 2=a x2 2+b y2 2+c z2 2=a x3 2+b y3 2+c z3 2=d ,a...

    Text Solution

    |

  6. if (x(1),x(2))^(2)+(y(1)-y(2))^(2)=a^(2), (x(2)-x(3))^(2)+(y(2)-y(3))^...

    Text Solution

    |

  7. Let A=[(cos^(- 1)x,cos^(- 1)y,cos^(- 1)z),(cos^(- 1)y,cos^(- 1)z,cos^...

    Text Solution

    |

  8. If y=(u)/(v), where u and v are functions of x, show that v^(3)(d^(2...

    Text Solution

    |

  9. If alpha&beta be the real roots of ax^(2)+bx+c=0 and s(n)=alpha^(n)+be...

    Text Solution

    |

  10. let a > 0 , d > 0 find the value of the determinant |[1/a,1/(a(a + d))...

    Text Solution

    |

  11. Let overset(to)(a(r))=x(r )hat(i)+y(r )hat(j)+z(r )hat(k),r=1,2,3 thre...

    Text Solution

    |

  12. If |(x^k,x^(k+2),x^(k+3)), (y^k,y^(k+2),y^(k+3)), (z^k,z^(k+2),z^(k+3)...

    Text Solution

    |

  13. If the determinant |(x+a,p+u,l+f),(y+b,q+v,m+g),(z+c,r+w,n+h)| splits ...

    Text Solution

    |

  14. If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-...

    Text Solution

    |

  15. If a,b,c are comples number and z=|{:(,0,-b,-c),(,bar(b),0,-a),(,bar(c...

    Text Solution

    |

  16. If f(x)=log(10)x and g(x)=e^(ln x) and h(x)=f [g(x)], then find the va...

    Text Solution

    |

  17. If A=[{:(,1,a),(,0,1):}] then find lim(n-oo) (1)/(n)A^(n)

    Text Solution

    |

  18. "Let" P=[{:(,"cos"(pi)/(9),"sin"(pi)/(9)),(,-"sin"(pi)/(9),"cos"(pi)/(...

    Text Solution

    |

  19. Let A=[{:(,1,1,1),(,1,1,1),(,1,1,1):}] , B=[{:(,2,-1,-1),(,-1,2,-1),(,...

    Text Solution

    |

  20. Let 'A' is (4xx4) matrix such that the sum of elements in each row is ...

    Text Solution

    |

  21. Let A=[{:(,x+lambda,x,x),(,x,x+lambda,x),(,x,x,x+lambda):}]then prove ...

    Text Solution

    |