Advertisements
Advertisements
प्रश्न
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)]`
उत्तर
We have A = `[(2, 4, -6),(7, 3, 5),(1, -2, 4)]`
Then A' = `[(2, 7, 1),(4, 3, -2),(-6, 5, 4)]`
Hence `("A" + "A'")/2 = 1/2 [(4, 11, -5),(11, 6, 3),(-5, 3, 8)]`
= `[(2, 11/2, (-5)/2),(11/2, 3, 3/2),((-5)/2, 3/2, 4)]`
and `("A" - "A'")/2 = 1/2 [(0, -3, -7),(3, 0, 7/2),(7, -7, 0)]`
= `[(0, (-3)/2, (-7)/2),(3/2, 0, 7/2),(7/2, (-7)/2, 0)]`
Therefore,
`("A" + "A'")/2 + ("A" - "A'")/2 = [(2, 11/2, (-5)/2),(11/2, 3, 3/2),((-5)/2, 3/2, 4)] + [(0, (-3)/2, (-7)/2),(3/2, 0, 7/2),(7/2, (-7)/2, 0)]`
= `[(2, 4, -6),(7, 3,5),(1,-2, 4)]`
= A
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 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'
Show that the matrix A = `[(0,1,-1),(-1,0,1),(1,-1,0)]` is a skew symmetric matrix.
For the matrix A = `[(1,5),(6,7)]` verify that (A - A') is a skew symmetric matrix.
if A =`((5,a),(b,0))` is symmetric matrix show that a = b
If a matrix A is both symmetric and skew-symmetric, then
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
If \[A = \begin{bmatrix}2 & 0 & - 3 \\ 4 & 3 & 1 \\ - 5 & 7 & 2\end{bmatrix}\] is expressed as the sum of a symmetric and skew-symmetric matrix, then the symmetric matrix is
If A and B are matrices of the same order, then ABT − BAT 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.
If A and B are symmetric matrices of the same order, then (AB′ –BA′) is a ______.
Show that A′A and AA′ are both symmetric matrices for any matrix A.
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.
The matrix `[(1, 0, 0),(0, 2, 0),(0, 0, 4)]` 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 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, B are Symmetric matrices of same order, then AB – BA is a
Let A and B be and two 3 × 3 matrices. If A is symmetric and B is skewsymmetric, then the matrix AB – BA is ______.
The value of |A|, if A = `[(0, 2x - 1, sqrt(x)),(1 - 2x, 0, 2sqrt(x)),(-sqrt(x), -2sqrt(x), 0)]`, where x ∈ R+, is ______.
