Advertisements
Advertisements
प्रश्न
If `[(2, 0),(5, 4)]` = P + Q, where P is symmetric, and Q is a skew-symmetric matrix, then Q is equal to ______.
विकल्प
`[(2, 5//2),(5//2, 4)]`
`[(0, 5//2),(-5//2, 0)]`
`[(0, -5//2),(5//2, 0)]`
`[(2, -5//2),(5//2, 4)]`
Advertisements
उत्तर
If `[(2, 0),(5, 4)]` = P + Q, where P is symmetric, and Q is a skew-symmetric matrix, then Q is equal to `underlinebb([(0, -5//2),(5//2, 0)])`.
Explanation:
Given `[(2, 0),(5, 4)]` = P + Q
For any matrix A, we have
A = `1/2 [(A + A^') + (A - A^')]`
= `(A + A^')/2 + (A - A^')/2`
where, `(A - A^')/2` is a symmetric matrix i.e., Q,
∴ Q = `1/2{[(2, 0),(5, 4)]-[(2, 5),(0, 4)]}`
= `1/2[(0, -5),(5, 0)]`
= `[(0, -5//2),(5//2, 0)]`
संबंधित प्रश्न
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'
If A' = `[(3, 4),(-1, 2),(0, 1)]` and B = `[(-1, 2, 1),(1, 2, 3)]`, then verify that (A – B)' = A' – B'
For the matrix A = `[(1, 5),(6, 7)]` verify that (A + A') is a symmetric matrix.
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
`[(3, 3, -1),(-2, -2, 1),(-4, -5, 2)]`
Write a square matrix which is both symmetric as well as skew-symmetric.
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
The matrix \[A = \begin{bmatrix}0 & - 5 & 8 \\ 5 & 0 & 12 \\ - 8 & - 12 & 0\end{bmatrix}\] is a
If the matrix `((6,-"x"^2),(2"x"-15 , 10))` is symmetric, find the value of x.
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 and B are two skew-symmetric matrices of same order, then AB is symmetric matrix if ______.
If A = `[(0, 1),(1, 1)]` and B = `[(0, -1),(1, 0)]`, show that (A + B)(A – B) ≠ A2 – B2
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 ______.
______ matrix is both symmetric and skew-symmetric matrix.
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 A and B are symmetric matrices of same order, then AB is symmetric if and only if ______.
If A is skew-symmetric matrix, then A2 is a symmetric matrix.
If P is of order 2 x 3 and Q is of order 3 x 2, then PQ is of order ____________.
If A and B are symmetric matrices of the same order, then ____________.
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, B are Symmetric matrices of same order, then AB – BA is a
If A = [aij] is a skew-symmetric matrix of order n, then ______.
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 ______.
If A and B are symmetric matrices of the same order, then AB – BA is ______.
