Advertisements
Advertisements
Question
The matrix \[A = \begin{bmatrix}0 & - 5 & 8 \\ 5 & 0 & 12 \\ - 8 & - 12 & 0\end{bmatrix}\] is a
Options
diagonal matrix
symmetric matrix
skew-symmetric matrix
scalar matrix
Advertisements
Solution
Given:
\[A^T = \begin{bmatrix}0 & - 5 & 8 \\ 5 & 0 & 12 \\ - 8 & - 12 & 0\end{bmatrix}^T \]
\[ = \begin{bmatrix}0 & 5 & - 8 \\ - 5 & 0 & - 12 \\ 8 & 12 & 0\end{bmatrix}\]
\[ = - 1\begin{bmatrix}0 & - 5 & 8 \\ 5 & 0 & 12 \\ - 8 & - 12 & 0\end{bmatrix}\]
\[ = - A\]
Therefore, matrix A is skew-symmetric matrix.
Hence, the correct option is (c).
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= `((3,5),(7,9))`is written as A = P + Q, where P is a symmetric matrix and Q is skew symmetric matrix, then write the matrix P.
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 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.
For the matrix A = `[(1, 5),(6, 7)]` verify that (A + A') 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)]`
If A and B are symmetric matrices, prove that AB – BA is a skew symmetric matrix.
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 ______.
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
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 is a square matrix, then AA is a
If A and B are symmetric matrices, then ABA is
If A = [aij] is a square matrix of even order such that aij = i2 − j2, then
Show that a matrix which is both symmetric and skew symmetric is a zero matrix.
If A and B are two skew-symmetric matrices of same order, then AB is symmetric matrix if ______.
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.
Express the matrix `[(2, 3, 1),(1, -1, 2),(4, 1, 2)]` as the sum of a symmetric and a skew-symmetric matrix.
If A is a symmetric matrix, then A3 is a ______ matrix.
If A is a skew-symmetric matrix, then A2 is a ______.
If A and B are symmetric matrices, then BA – 2AB is a ______.
If A and B are symmetric matrices of same order, then AB is symmetric if and only if ______.
If P is of order 2 x 3 and Q is of order 3 x 2, then PQ is of order ____________.
If A `= [(6,8,5),(4,2,3),(9,7,1)]` is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is ____________.
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 ______.
Let A = `[(2, 3),(a, 0)]`, a ∈ R be written as P + Q where P is a symmetric matrix and Q is skew-symmetric matrix. If det(Q) = 9, then the modulus of the sum of all possible values of determinant of P is equal to ______.
If A and B are symmetric matrices of the same order, then AB – BA is ______.
