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

Matrix A = `[(0,2b,-2),(3,1,3),(3a,3,-1)]`is given to be symmetric, find values of a and b


If A = `[(-1, 2, 3),(5, 7, 9),(-2, 1, 1)]` and B = `[(-4, 1, -5),(1, 2, 0),(1, 3, 1)]`, then verify that (A – B)' = A' – B'


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


For the matrices A and B, verify that (AB)′ = B'A', where A = `[(1),(-4),(3)]`, B = `[(-1, 2, 1)]`


For the matrices A and B, verify that (AB)′ = B'A' where A = `[(0),(1),(2)]`, B = `[(1, 5, 7)]`


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


For the matrix A = `[(1, 5),(6, 7)]` verify that (A + A') is a symmetric matrix.


For the matrix A = `[(1, 5),(6, 7)]`, verify that (A – A') is a skew symmetric matrix.


If \[A = \begin{bmatrix}1 & 2 \\ 0 & 3\end{bmatrix}\] is written as B + C, where B is a symmetric matrix and C is a skew-symmetric matrix, then B is equal to.


If A is a square matrix, then AA is a


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


Express the matrix A as the sum of a symmetric and a skew-symmetric matrix, where A = `[(2, 4, -6),(7, 3, 5),(1, -2, 4)]`


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


If A and B are symmetric matrices of the same order, then (AB′ –BA′) is a ______.


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


The matrix `[(0, -5, 8),(5, 0, 12),(-8, -12, 0)]` is a ______.


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


If A and B are symmetric matrices, then BA – 2AB is a ______.


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


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


If A and B are symmetric matrices of the same order, then ____________.


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


If ax4 + bx3 + cx2 + dx + e = `|(2x, x - 1, x + 1),(x + 1, x^2 - x, x - 1),(x - 1, x + 1, 3x)|`, then the value of e is ______.


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


If `[(2, 0),(5, 4)]` = P + Q, where P is symmetric, and Q is a skew-symmetric matrix, then Q is equal to ______.


Which of the following is correct?


A square matrix \[A=[a_{ij}]_{n\times n}\] is symmetric when which condition holds?


For a symmetric matrix \[A=[a_{ij}]_{n\times n}\], which entrywise relation is true for all \[i\] and \[j\]?


A square matrix \[A=[a_{ij}]_{n\times n}\] is skew-symmetric when which condition holds?


For a skew-symmetric matrix \[A=[a_{ij}]_{n\times n}\], which relation holds for all \[i\] and \[j\]?


What must be true of every diagonal element of a skew-symmetric matrix?


Which transpose property justifies the step \[(A+A^T)^T=A^T+(A^T)^T\]?


Which identity is used to replace \[(A^T)^T\] by \[A\] when proving that \[A+A^T\] is symmetric?


For \[B=\begin{bmatrix}2&-2&-4\\-1&3&4\\1&-2&-3\end{bmatrix}\], what is its symmetric part \[P=\frac{1}{2}(B+B^T)\]?


How many decompositions of a square matrix into a symmetric part and a skew-symmetric part are possible?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×