Advertisements
Advertisements
प्रश्न
If A and B are matrices of same order, then (AB′ – BA′) is a ______.
विकल्प
Skew-symmetric matrix
Null matrix
Symmetric matrix
Unit matrix
Advertisements
उत्तर
If A and B are matrices of same order, then (AB′ – BA′) is a skew-symmetric matrix.
Explanation:
Let P = (AB' – BA')
P' = (AB' – BA')'
= (AB')' – (BA')'
= (B')A' – (A')'B' ......[∵ (AB)' = B'A']
= BA' – AB'
= – (AB' – BA')
= – P
P' = – P
So it is a 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 = `[(cos α, sin α), (-sin α, cos α)]`, then verify that A' A = I
Show that the matrix A = `[(1, -1, 5),(-1, 2, 1),(5, 1, 3)]` is a symmetric matrix.
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:
`[(3, 5),(1, -1)]`
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)]`
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
`[(1, 5),(-1, 2)]`
If A and B are symmetric matrices, prove that AB – BA is a skew symmetric matrix.
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.
Show that all the diagonal elements of a skew symmetric matrix are zero.
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.
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 and B are symmetric matrices, then ABA is
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 = `[(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 `[(0, -5, 8),(5, 0, 12),(-8, -12, 0)]` is a ______.
If A is a symmetric matrix, then A3 is a ______ matrix.
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.
If A is skew-symmetric matrix, then A2 is a symmetric matrix.
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?
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 ______.
Number of symmetric matrices of order 3 × 3 with each entry 1 or – 1 is ______.
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 ______.
