Advertisements
Advertisements
प्रश्न
If A' = `[(3, 4),(-1, 2),(0, 1)]` and B = `[(-1, 2, 1),(1, 2, 3)]`, then verify that (A + B)' = A' + B'
Advertisements
उत्तर
Given, A' = `[(3, 4),(-1, 2),(0, 1)]` and B = `[(-1, 2, 1),(1, 2, 3)]`
Then, A = `[(3, -1, 0),(4, 2, 1)]` and B' = `[(-1, 1),(2, 2),(1, 3)]` ...[∵ (A)' = A]
Now, (A + B) = `[(3, -1, 0),(4, 2, 1)] + [(-1, 2, 1),(1, 2, 3)]`
= `[(3 - 1, -1 + 2, 0 + 1),(4 + 1, 2 + 2, 1 + 3)]`
= `[(2, 1, 1),(5, 4, 4)]`
Then, (A + B)' = `[(2, 5),(1, 4),(1, 4)]` ...(i)
A' + B' = `[(3, 4),(-1, 2),(0, 1)] + [(-1, 1),(2, 2),(1, 3)]`
= `[(3 - 1, 4 + 1),(-1 + 2, 2 + 2), (0 + 1, 1 + 3)]`
= `[(2, 5),(1, 4),(1, 4)]` ...(ii)
Equations (i) and (ii) prove that,
(A + B)' = A' + B'
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' = `[(-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 α, sin α), (-sin α, cos α)]`, then verify that A' A = I
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 symmetric matrix.
For the matrix A = `[(1, 5),(6, 7)]`, verify that (A – A') is a skew symmetric matrix.
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:
`[(3, 3, -1),(-2, -2, 1),(-4, -5, 2)]`
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 the matrix A is both symmetric and skew symmetric, then ______.
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
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 is a square matrix, then AA is a
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 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
The matrix `[(1, 0, 0),(0, 2, 0),(0, 0, 4)]` is a ______.
If A is a symmetric matrix, then A3 is a ______ matrix.
If A is symmetric matrix, then B′AB is ______.
If A and B are symmetric matrices of same order, then AB is symmetric if and only if ______.
If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.
If A = `[(3, "x" - 1),(2"x" + 3, "x" + 2)]` is a symmetric matrix, then x = ____________.
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 ______.
For what value of k the matrix `[(0, k),(-6, 0)]` is a skew symmetric matrix?
Which of the following is correct?
