Advertisements
Advertisements
Question
If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.
Options
True
False
Solution
This statement is True.
Explanation:
Let A, B and C be three matrices of the same order.
Given that A' = A, B' = B and C' = C
Let P = A + B + C
⇒ P' = (A + B + C)'
= A' + B' + C'
= A + B + C
= P
So, A + B + C is also a symmetric matrix.
APPEARS IN
RELATED QUESTIONS
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' [(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)'
For the matrices A and B, verify that (AB)′ = B'A' where `A =[(0), (1),(2)] , B =[1 , 5, 7]`
If A = `[(cos alpha, sin alpha), (-sin alpha, cos alpha)]` then verify that A' A = I
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:
`[(3,3,-1),(-2,-2,1),(-4,-5,2)]`
If A and B are symmetric matrices, prove that AB − BA is a skew symmetric matrix.
Find the values of x, y, z if the matrix `A = [(0,2y,z),(x,y,-z),(x , -y,z)]` satisfy the equation A'A = I.
if A =`((5,a),(b,0))` is symmetric matrix show that a = b
If a matrix A is both symmetric and skew-symmetric, 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
The matrix \[A = \begin{bmatrix}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{bmatrix}\] is
Show that a matrix which is both symmetric and skew symmetric is a zero matrix.
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 and B are matrices of same order, then (AB′ – BA′) is a ______.
If A and B are symmetric matrices of same order, then AB is symmetric if and only if ______.
If A is any square matrix, then which of the following is skew-symmetric?
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 ____________.
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 ______.
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 ______.
Let A and B be and two 3 × 3 matrices. If A is symmetric and B is skewsymmetric, then the matrix AB – BA is ______.
If A and B are symmetric matrices of the same order, then AB – BA is ______.
