Home
Class 12
MATHS
If A = [(3,-5),(-4,2)] then show that A+...

If `A = [(3,-5),(-4,2)]` then show that A+A' is a symmetric matrix.

Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

If A={:[(2,3),(4,5)], prove that A-A^(T) is a skew-symmetric matrix.

If A is a matrix of order n such that A^(T)A=I and X is any matrix such that X=(A+I)^(-1) (A-I) , then show that X is skew symmetric matrix.

For the matrix A=[(1,5),(6,7)] , verify that (i) (A+A') is a symmetric matrix (ii) (A-A') is a skew symmetric matrix

If A = [[3,-5],[-4,2]] ,show that A^2 -5A-14I =0.

If A = [[2,3], [4,5]] , prove that A - A^(T) is a skew-symmetric matrix.

If A and B are non-singular symmetric matrices such that AB=BA , then prove that A^(-1) B^(-1) is symmetric matrix.

Express the matrix A={:[(4,2,-1),(3,5,7),(1,-2,1)]:} as the sum of a symmetric matrix and a skew-symmetric matrix.

If matrix A=[(0,1,-1),(4,-3,4),(3,-3,4)]=B+C , where B is symmetric matrix and C is skew-symmetric matrix, then find matrices B and C.

Let A be a square matrix. Then prove that (i) A + A^T is a symmetric matrix and, (ii) A -A^T is a skew-symmetric matrix

If A = [(4,5),(5,6)] show that, A^(2) = 10A + I where I is the unit matrix or order 2. Hence, find the inverse of A.

UNITED BOOK HOUSE-SET 18-EXERCISE
  1. Let us consider a function f : R rarrR, defined by f(x) =x^3 - 6. Show...

    Text Solution

    |

  2. Show that Sec^2 (cot^-1(2)) + cosec^2(tan^-1 (3)) = 2 13/36

    Text Solution

    |

  3. If A = [(3,-5),(-4,2)] then show that A+A' is a symmetric matrix.

    Text Solution

    |

  4. Without expanding show that the determinant |(1,a,a^2),(-1,2,4),(1,x,x...

    Text Solution

    |

  5. Examine the applicability of lagrange's Mean value theorem for the fun...

    Text Solution

    |

  6. If sin^(-1) ((x^2-y^2)/(x^2+y^2))=k, k is a constant, then prove that ...

    Text Solution

    |

  7. Evaluate: int((cosx+xsinx)/(x(x+cosx)))dx.

    Text Solution

    |

  8. Using the method of differentail find the approximate value of sqrt 0....

    Text Solution

    |

  9. If veca = 3hati - 2hatj + hatk and vecb = hati - 3hatj + hatk find vec...

    Text Solution

    |

  10. If direction ratios of two lines are (a,b,c)and (b-c,c-a,a-b), find an...

    Text Solution

    |

  11. Find the binomial distribution for which the mean and variance are 12 ...

    Text Solution

    |

  12. If for two events A and B, P(A) = P(A/B) = 1/4 and P(B/A) = 1/2, show ...

    Text Solution

    |

  13. if tan ^(-1) x+tan ^(-1)y+tan ^(-1) z=pi/2 and x+y+z= sqrt3 , then sho...

    Text Solution

    |

  14. If A = [(1,0),(0,1)] and B = [(0,1),(-1,0)], show that (pA + qB) (pA -...

    Text Solution

    |

  15. If x,y,z are all distinct and if abs((x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^...

    Text Solution

    |

  16. Solve for x : |(x,a,b),(a,x,b),(a,b,x)| = 0

    Text Solution

    |

  17. Find the derivation of sin^-1 (x^2 sqrt(1-x) - sqrtx sqrt(1-x^4)) with...

    Text Solution

    |

  18. Evaluate : int(x^2dx)/((x sin x + cos x)^2)

    Text Solution

    |

  19. Solve: (dy)/(dx) +x(sin2y) = x^3 cos^2 y, y(0) = then y(1) equal to

    Text Solution

    |

  20. The temperature T of a cooling object drops at a rate proportional to ...

    Text Solution

    |