Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let A = `[(0, "a", 3),(2, "b", -1),("c", 1, 0)]`
A = `[(0, 2, "c"),("a", "b", 1),(3, -1, 0)]`
For skew symmetric matrix, A' = – A.
⇒ `[(0, 2, "c"),("a", "b", 1),(3, -1, 0)] = -[(0, "a", 3),(2, "b", -1),("c", 1, 0)]`
⇒ `[(0, 2, "c"),("a", "b", 1),(3, -1, 0)] = [(0, -"a", -3),(-2, -"b", 1),(-"c", -1, 0)]`
Equating the corresponding elements, we get
a = – 2, b = – b
⇒ 2b = 0
⇒ b = 0
And c = – 3
Hence, a = – 2, b = 0 and c = – 3.
APPEARS IN
संबंधित प्रश्न
Matrix A = `[(0,2b,-2),(3,1,3),(3a,3,-1)]`is given to be symmetric, find values of a and b
if `A' [(3,4),(-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)]`
Show that the matrix B'AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.
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.
Write a square matrix which is both symmetric as well as skew-symmetric.
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
The matrix \[A = \begin{bmatrix}0 & - 5 & 8 \\ 5 & 0 & 12 \\ - 8 & - 12 & 0\end{bmatrix}\] is a
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 ______.
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.
The matrix `[(1, 0, 0),(0, 2, 0),(0, 0, 4)]` is a ______.
The matrix `[(0, -5, 8),(5, 0, 12),(-8, -12, 0)]` is a ______.
If A and B are matrices of same order, then (AB′ – BA′) is a ______.
Sum of two skew-symmetric matrices is always ______ matrix.
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 AB – BA is a ______.
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 is skew-symmetric matrix, then A2 is a symmetric matrix.
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 `= [(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 ____________.
The diagonal elements of a skew symmetric matrix are ____________.
If A = [aij] is a skew-symmetric matrix of order n, then ______.
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 ______.
