Advertisements
Advertisements
Question
The matrix `[(0, -5, 8),(5, 0, 12),(-8, -12, 0)]` is a ______.
Options
Diagonal matrix
Symmetric matrix
Skew-symmetric matrix
Scalar matrix
Advertisements
Solution
The matrix `[(0, -5,8),(5, 0, 12),(-8, -12, 0)]` is a skew symmetric matrix.
Explanation:
Let A = `[(0, -5, 8),(5, 0, 12),(-8, -12, 0)]`
A' = `[(0, 5, -8),(-5, 0, -12),(8, 12, 0)]`
⇒ A' = `-[(0, -5, 8),(5, 0, 12),(-8, -12, 0)]` = – A
A' = – A
So A is a skew-symmetric matrix.
APPEARS IN
RELATED QUESTIONS
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 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 = `[(0),(1),(2)]`, B = `[(1, 5, 7)]`
If A = `[(cos α, sin α), (-sin α, cos α)]`, then verify that A' A = I
For the matrix A = `[(1, 5),(6, 7)]` verify that (A + A') is a symmetric matrix.
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:
`[(3, 5),(1, -1)]`
if A =`((5,a),(b,0))` is symmetric matrix show that a = b
The matrix \[\begin{bmatrix}0 & 5 & - 7 \\ - 5 & 0 & 11 \\ 7 & - 11 & 0\end{bmatrix}\] is
If A = [aij] is a square matrix of even order such that aij = i2 − j2, then
The matrix \[A = \begin{bmatrix}0 & - 5 & 8 \\ 5 & 0 & 12 \\ - 8 & - 12 & 0\end{bmatrix}\] is a
The matrix \[A = \begin{bmatrix}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{bmatrix}\] is
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.
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 = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, and A–1 = A′, find value of α
If A, B are square matrices of same order and B is a skew-symmetric matrix, show that A′BA is skew-symmetric.
Express the matrix `[(2, 3, 1),(1, -1, 2),(4, 1, 2)]` as the sum of a symmetric and a skew-symmetric matrix.
Sum of two skew-symmetric matrices is always ______ matrix.
If A is a skew-symmetric matrix, then A2 is a ______.
If A and B are symmetric matrices, then AB – BA is a ______.
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 and B are any two matrices of the same order, then (AB)′ = A′B′.
AA′ is always a symmetric matrix for any matrix A.
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
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 ______.
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?
Which of the following is correct?
