Advertisements
Advertisements
प्रश्न
If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.
पर्याय
True
False
Advertisements
उत्तर
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
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'
For the matrices A and B, verify that (AB)′ = B'A', where A = `[(1),(-4),(3)]`, B = `[(-1, 2, 1)]`
If A = `[(cos α, sin α), (-sin α, cos α)]`, then verify that A' A = I
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, 5),(1, -1)]`
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
`[(3, 3, -1),(-2, -2, 1),(-4, -5, 2)]`
Show that the matrix B'AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.
If \[A = \begin{bmatrix}1 & 2 \\ 0 & 3\end{bmatrix}\] is written as B + C, where B is a symmetric matrix and C is a skew-symmetric matrix, then B is equal to.
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 and B are two matrices of order 3 × m and 3 × n respectively and m = n, then the order of 5A − 2B is
The matrix `[(0, -5, 8),(5, 0, 12),(-8, -12, 0)]` is a ______.
If A is a skew-symmetric matrix, then A2 is a ______.
If A and B are symmetric matrices, then BA – 2AB is a ______.
If A and B are any two matrices of the same order, then (AB)′ = A′B′.
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 ____________.
The diagonal elements of a skew symmetric matrix are ____________.
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 ______.
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 ______.
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 ______.
A square matrix \[A=[a_{ij}]_{n\times n}\] is symmetric when which condition holds?
For a symmetric matrix \[A=[a_{ij}]_{n\times n}\], which entrywise relation is true for all \[i\] and \[j\]?
A square matrix \[A=[a_{ij}]_{n\times n}\] is skew-symmetric when which condition holds?
If \[C=A-A^T\] for a square matrix \[A\], what is \[C^T\]?
Which expression writes any square matrix \[A\] as the sum of a symmetric and a skew-symmetric matrix?
For \[B=\begin{bmatrix}2&-2&-4\\-1&3&4\\1&-2&-3\end{bmatrix}\], what is its symmetric part \[P=\frac{1}{2}(B+B^T)\]?
For \[B=\begin{bmatrix}2&-2&-4\\-1&3&4\\1&-2&-3\end{bmatrix}\], what is its skew-symmetric part \[Q=\frac{1}{2}(B-B^T)\]?
