Advertisements
Advertisements
प्रश्न
If A is skew-symmetric, then kA is a ______. (k is any scalar)
उत्तर
If A is skew-symmetric, then kA is a skew-symmetric matrix. (k is any scalar)
Explanation:
Given A is skew-symmetric matrix
∴ A' = –A
∴ (kA)' = kA'
= k(–A)
= – kA
∴ (kA) is also skew-symmetric matrix.
APPEARS IN
संबंधित प्रश्न
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' [(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 = `[(cos alpha, sin alpha), (-sin alpha, cos alpha)]` then verify that A' A = I
Find `1/2` (A + A') and `1/2` (A -A') When `A = [(0, a, b),(-a,0,c),(-b,-c,0)]`
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
`[(6, -2,2),(-2,3,-1),(2,-1,3)]`
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
`[(3,3,-1),(-2,-2,1),(-4,-5,2)]`
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 =`((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 the matrix `((6,-"x"^2),(2"x"-15 , 10))` is symmetric, find the value of x.
Show that a matrix which is both symmetric and skew symmetric is a zero matrix.
If A = `[(0, 1),(1, 1)]` and B = `[(0, -1),(1, 0)]`, show that (A + B)(A – B) ≠ A2 – B2
If A = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, and A–1 = A′, find value of α
Express the matrix `[(2, 3, 1),(1, -1, 2),(4, 1, 2)]` as the sum of a symmetric and a skew-symmetric matrix.
The matrix `[(1, 0, 0),(0, 2, 0),(0, 0, 4)]` is a ______.
______ matrix is both symmetric and skew-symmetric matrix.
If A is symmetric matrix, then B′AB is ______.
If A and B are any two matrices of the same order, then (AB)′ = A′B′.
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 is any square matrix, then which of the following is skew-symmetric?
The diagonal elements of a skew symmetric matrix are ____________.
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 ______.
