मराठी

If A and B are two skew symmetric matrices of same order, then AB is symmetric matrix if ______.

Advertisements
Advertisements

प्रश्न

If A and B are two skew-symmetric matrices of same order, then AB is symmetric matrix if ______.

रिकाम्या जागा भरा
Advertisements

उत्तर

If A and B are two skew-symmetric matrices of same order, then AB is symmetric matrix if AB = BA.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Matrices - Solved Examples [पृष्ठ ५२]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
पाठ 3 Matrices
Solved Examples | Q 13 | पृष्ठ ५२

संबंधित प्रश्‍न

If A is a skew symmetric matric of order 3, then prove that det A  = 0


If A' = `[(3, 4),(-1, 2),(0, 1)]` and B = `[(-1, 2, 1),(1, 2, 3)]`, then verify that (A – B)' = A' – B'


If A' = `[(-2, 3),(1, 2)]` and B = `[(-1, 0),(1, 2)]`, then find (A + 2B)'


If A = `[(sin α, cos α), (-cos α, sin α)]`, then verify that A'A = I


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


Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

`[(6, -2, 2),(-2, 3, -1),(2, -1, 3)]`


Find the values of x, y, z if the matrix A = `[(0, 2y, z),(x, y, -z),(x, -y, z)]` satisfy the equation A'A = I.


If the matrix A is both symmetric and skew symmetric, then ______.


Show that all the diagonal elements of a skew symmetric matrix are zero.


For what value of x, is the matrix \[A = \begin{bmatrix}0 & 1 & - 2 \\ - 1 & 0 & 3 \\ x & - 3 & 0\end{bmatrix}\] a skew-symmetric matrix?


If a matrix A is both symmetric and skew-symmetric, then


If the matrix `((6,-"x"^2),(2"x"-15 , 10))` is symmetric, find the value of x.


Let A = `[(2, 3),(-1, 2)]`. Then show that A2 – 4A + 7I = O. Using this result calculate A5 also.


Show that A′A and AA′ are both symmetric matrices for any matrix A.


If A = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, and A–1 = A′, find value of α


If the matrix `[(0, "a", 3),(2, "b", -1),("c", 1, 0)]`, is a skew symmetric matrix, find the values of a, b and c.


______ matrix is both symmetric and skew-symmetric matrix.


Sum of two skew-symmetric matrices is always ______ matrix.


If A is a skew-symmetric matrix, then A2 is a ______.


If A is skew-symmetric, then kA is a ______. (k is any scalar)


If A is symmetric matrix, then B′AB is ______.


If A and B are symmetric matrices of same order, then AB is symmetric if and only if ______.


AA′ is always a symmetric matrix for any matrix A.


If A is skew-symmetric matrix, then A2 is a symmetric matrix.


If A is any square matrix, then which of the following is skew-symmetric?


If A `= [(6,8,5),(4,2,3),(9,7,1)]` is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is ____________.


The diagonal elements of a skew symmetric matrix are ____________.


Let A and B be and two 3 × 3 matrices. If A is symmetric and B is skewsymmetric, then the matrix AB – BA is ______.


The value of |A|, if A = `[(0, 2x - 1, sqrt(x)),(1 - 2x, 0, 2sqrt(x)),(-sqrt(x), -2sqrt(x), 0)]`, where x ∈ R+, is ______.


Which of the following is correct?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×