Advertisements
Advertisements
Question
Sum of two skew-symmetric matrices is always ______ matrix.
Advertisements
Solution
Sum of two skew-symmetric matrices is always skew-symmetric matrix.
Explanation:
Let A and B be any two matrices
∴ For skew-symmetric matrices
A = –A' ......(i)
And B = –B' ......(ii)
Adding (i) and (ii) we get
A + B = –A' – B'
⇒ A + B = –(A' + B')
So A + B is skew-symmetric matrix.
APPEARS IN
RELATED QUESTIONS
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' = `[(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)'
For the matrices A and B, verify that (AB)′ = B'A', where A = `[(1),(-4),(3)]`, B = `[(-1, 2, 1)]`
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:
`[(3, 5),(1, -1)]`
Show that the matrix B'AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.
If the matrix A is both symmetric and skew symmetric, then ______.
If A = [aij] is a square matrix of even order such that aij = i2 − j2, then
If \[A = \begin{bmatrix}2 & 0 & - 3 \\ 4 & 3 & 1 \\ - 5 & 7 & 2\end{bmatrix}\] is expressed as the sum of a symmetric and skew-symmetric matrix, then the symmetric matrix is
If A and B are two matrices of order 3 × m and 3 × n respectively and m = n, then the order of 5A − 2B is
Show that a matrix which is both symmetric and skew symmetric is a zero matrix.
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)]`
If A = `[(0, 1),(1, 1)]` and B = `[(0, -1),(1, 0)]`, show that (A + B)(A – B) ≠ A2 – B2
If A is a symmetric matrix, then A3 is a ______ matrix.
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 and B are symmetric matrices of the same order, then ____________.
The diagonal elements of a skew symmetric matrix are ____________.
If A, B are Symmetric matrices of same order, then AB – BA is a
If A = [aij] is a skew-symmetric matrix of order n, then ______.
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 ______.
If `[(2, 0),(5, 4)]` = P + Q, where P is symmetric, and Q is a skew-symmetric matrix, then Q is equal to ______.
For what value of k the matrix `[(0, k),(-6, 0)]` is a skew symmetric matrix?
If A and B are symmetric matrices of the same order, then AB – BA is ______.
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 \[j\]?
Which expression writes any square matrix \[A\] as the sum of a symmetric and a skew-symmetric matrix?
For \[B=\begin{bmatrix}2&-2&-4\\-1&3&4\\1&-2&-3\end{bmatrix}\], what is its skew-symmetric part \[Q=\frac{1}{2}(B-B^T)\]?
