Advertisements
Advertisements
प्रश्न
If A and B are symmetric matrices, then BA – 2AB is a ______.
Advertisements
उत्तर
If A and B are symmetric matrices, then BA – 2AB is a neither a symmetric nor a skew-symmetric matrix.
Explanation:
Let Q = (BA – 2AB)
Q' = (BA – 2AB)'
= (BA)' – (2AB)'
= A'B' – 2(AB)' .....[∵ (kA)' = kA']
= A'B' – 2B'A'
= AB – 2BA .....[∵ A' = A an B' = B]
= –(2BA – AB)
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= `((3,5),(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' = `[(-2, 3),(1, 2)]` and B = `[(-1, 0),(1, 2)]`, then find (A + 2B)'
Show that the matrix A = `[(1, -1, 5),(-1, 2, 1),(5, 1, 3)]` is a symmetric matrix.
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.
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)]`
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
`[(6, -2, 2),(-2, 3, -1),(2, -1, 3)]`
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
`[(1, 5),(-1, 2)]`
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
The matrix \[\begin{bmatrix}0 & 5 & - 7 \\ - 5 & 0 & 11 \\ 7 & - 11 & 0\end{bmatrix}\] is
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
If A and B are matrices of the same order, then ABT − BAT is a
Show that a matrix which is both symmetric and skew symmetric is a zero matrix.
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 matrices of same order, then (AB′ – BA′) is a ______.
If A is a skew-symmetric matrix, then A2 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 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 ____________.
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 ______.
Number of symmetric matrices of order 3 × 3 with each entry 1 or – 1 is ______.
Which of the following is correct?
