Home
Class 12
MATHS
The inverse of a symmetric matrix is :...

The inverse of a symmetric matrix is :

A

symmetric

B

skew-symmetric

C

diagonal matrix

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    BETTER CHOICE PUBLICATION|Exercise SOLVED EXAMPLES (SECTION II) (SHORT ANSWER TYPE QUESTIONS)|6 Videos

  • DETERMINANTS

    BETTER CHOICE PUBLICATION|Exercise SOLVED EXAMPLES (SECTION III) |9 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEARS BOARDS QUESTIONS FOR PRACTICE (MULTIPLE CHOICE QUESTIONS)|94 Videos

  • DIFFERENTIAL EQUATIONS

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEARS BOARD.S QUESTIONS FOR PRACTICE|50 Videos

Similar Questions

Explore conceptually related problems

Show that the positive odd integral powers of a kew-symmetric matrix are skew-symmetric and positive even integral powers of a skew-symmetric matrix are symmetric.

Express A=[(2,3,5),(0,2,9),(3,2,8)] as the sum of a symmetric matrix and a skew-symmetric matrix.

Express A= [[2,3,,5],[0,2,,9],[3,2,,8]] as the sum of a symmetric matrix and skew- symmetric matrix.

Each diagonal element of a skew symmetric matrix is

If each of the three matrices of the same order are symmetric then their sum is a symmetric matrix .

If A and B are symmetric matrices, then A B A is (a) symmetric matrix (b) skew-symmetric matrix (c) diagonal matrix (d) scalar matrix

If A is a skew-symmetric matrix and n is odd positive integer, then A^n is a skew-symmetric matrix a symmetric matrix a diagonal matrix none of these

If A is skew symmetric matrix, then A^(2) is a symmetric matrix .

Fill in the blanks: If A is a symmetric matrix then A^2 is a …. Matrix.

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

BETTER CHOICE PUBLICATION-DETERMINANTS -ASSIGNMENT (PREVIOUS YEAR.S BOARD QUESTIONS FOR PRACTICE )
  1. The inverse of a symmetric matrix is :

    Text Solution

    |

  2. Using the properties of determinants, prove that : |[[x+a,b,c],[a,x+b,...

    Text Solution

    |

  3. Prove that: |[a+b+2c,a,b],[c,b+c+2a,b],[c,a,c+a+2b]|= 2(a+b+c)^3

    Text Solution

    |

  4. Solve |(x+1,2,3),(3,x+2,1),(1,2,x+3)|=0

    Text Solution

    |

  5. Solve by matrix method 3/x+4/y+7/z=14 2/x-1/y+3/z=4 1/x+2/y-3/z=...

    Text Solution

    |

  6. Using the properties of determinants show that : |[[-bc,b^2+bc,c^2+bc]...

    Text Solution

    |

  7. Using the properties of determinants show that : |[[1,1,1],[a^2,b^2,c^...

    Text Solution

    |

  8. Using the properties of determinants show that : |[[1, a^2+bc, a^3],[1...

    Text Solution

    |

  9. Using matrices , solve the following system of linear equations 5x -...

    Text Solution

    |

  10. Solve by matrix method 2x -y +z =-1 -x +2y -z =4 x-y + 2z =-3

    Text Solution

    |

  11. Without expanding the determinant, show that : (frac{1}{a}+frac{1}{b}+...

    Text Solution

    |

  12. Prove that |[[a,b,c],[a^2,b^2,c^2],[a^3,b^3,c^3]]|= abc (a-b)(b-c)(c-a...

    Text Solution

    |

  13. Prove that |[[x,y,z],[x^2,y^2,z^2],[x^3,y^3,z^3]]|= xyz (x-y)(y-z)(z-x...

    Text Solution

    |

  14. Solve by matrix method : x+y = 3 , y +z =4 , z + x =5

    Text Solution

    |

  15. Prove that: |[-a^2, ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]|=4a^2b^2c^2

    Text Solution

    |

  16. By using properties of determinants, show that : |[x+y+2z,x,y],[z,y+...

    Text Solution

    |

  17. Solve the following system of linear equations by matrix method : 2x +...

    Text Solution

    |

  18. Solve the following system of linear equations by matrix method : 2x -...

    Text Solution

    |

  19. If A= [[4,1,1],[1,4,1],[1,1,4]], then show that |2A| = 8 |A|.

    Text Solution

    |

  20. If A= [[2,1,1],[1,2,1],[1,1,2]], then show that |4A| = 64 |A|.

    Text Solution

    |

  21. Using the properties of determinant, show that :|[a^2+1,ab,ac],[ab,b^2...

    Text Solution

    |