Advertisements
Advertisements
प्रश्न
Sum of two skew-symmetric matrices is always ______ matrix.
उत्तर
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
संबंधित प्रश्न
If A is a skew symmetric matric of order 3, then prove that det A = 0
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'
For the matrices A and B, verify that (AB)′ = B'A' where `A =[(1),(-4), (3)], B = [-1, 2 1]`
If A = `[(cos alpha, sin alpha), (-sin alpha, cos alpha)]` then verify that A' A = I
If A = `[(sin alpha, cos alpha), (-cos alpha, sin alpha)]` then verify that A'A = I
For the matrix A = `[(1,5),(6,7)]` verify that (A - A') 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)]`
If the matrix A is both symmetric and skew symmetric, then ______.
Show that all the diagonal elements of a skew symmetric matrix are zero.
if A =`((5,a),(b,0))` is symmetric matrix show that a = b
If A and B are symmetric matrices of the same order, write whether AB − BA is symmetric or skew-symmetric or neither of the two.
The matrix \[\begin{bmatrix}0 & 5 & - 7 \\ - 5 & 0 & 11 \\ 7 & - 11 & 0\end{bmatrix}\] is
If A is a square matrix, then AA is a
If A = [aij] is a square matrix of even order such that aij = i2 − j2, then
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
The matrix \[A = \begin{bmatrix}0 & - 5 & 8 \\ 5 & 0 & 12 \\ - 8 & - 12 & 0\end{bmatrix}\] is a
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.
If A and B are symmetric matrices of the same order, then (AB′ –BA′) is a ______.
If A and B are two skew-symmetric matrices of same order, then AB is symmetric matrix if ______.
Show that A′A and AA′ are both symmetric matrices for any matrix A.
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.
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 P is of order 2 x 3 and Q is of order 3 x 2, then PQ is of order ____________.
If A and B are symmetric matrices of the same order, then ____________.
If A = `[(3, "x" - 1),(2"x" + 3, "x" + 2)]` is a symmetric matrix, then x = ____________.
If A, B are Symmetric matrices of same order, then AB – BA is a
