Advertisements
Advertisements
प्रश्न
For the matrices A and B, verify that (AB)′ = B'A' where A = `[(0),(1),(2)]`, B = `[(1, 5, 7)]`
Advertisements
उत्तर
Given, A = `[(0),(1),(2)]` and B = `[(1, 5, 7)]`
So, AB = `[(0),(1),(2)] xx [(1, 5, 7)]`
= `[(0 xx 1, 0 xx 5, 0 xx 7),(1 xx 1, 1 xx 5, 1 xx 7),(2 xx 1, 2 xx 5, 2 xx 7)]`
= `[(0, 0, 0), (1, 5, 7),(2, 10, 14)]`
Now, (AB)' = `[(0, 1, 2),(0, 5, 10),(0, 7, 14)]` ...(i)
So, A' = `[(0, 1, 2)]` and B' = `[(1),(5),(7)]`
Now, B'A' = `[(1),(5),(7)] xx [(0, 1, 2)]`
= `[(1 xx 0, 1 xx 1, 1 xx 2), (5 xx 0, 5 xx 1, 5 xx 2), (7 xx 0, 7 xx 1, 7 xx 2)]`
= `[(0, 1, 2),(0, 5, 10),(0, 7, 14)]` ...(ii)
Equations (i) and (ii) prove that,
∴ (AB)' = B'A'
APPEARS IN
संबंधित प्रश्न
If A is a skew symmetric matric of order 3, then prove that det A = 0
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.
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)]`
If A and B are symmetric matrices, prove that AB – BA is a skew symmetric matrix.
Show that the matrix B'AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.
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 ______.
if A =`((5,a),(b,0))` is symmetric matrix show that a = b
Write a square matrix which is both symmetric as well as skew-symmetric.
The matrix \[\begin{bmatrix}0 & 5 & - 7 \\ - 5 & 0 & 11 \\ 7 & - 11 & 0\end{bmatrix}\] is
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 \[A = \begin{bmatrix}0 & - 5 & 8 \\ 5 & 0 & 12 \\ - 8 & - 12 & 0\end{bmatrix}\] is a
If the matrix `((6,-"x"^2),(2"x"-15 , 10))` is symmetric, find the value of x.
Let A = `[(2, 3),(-1, 2)]`. Then show that A2 – 4A + 7I = O. Using this result calculate A5 also.
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 the matrix `[(0, "a", 3),(2, "b", -1),("c", 1, 0)]`, is a skew symmetric matrix, find the values of a, b and c.
If A, B are square matrices of same order and B is a skew-symmetric matrix, show that A′BA is skew-symmetric.
The matrix `[(1, 0, 0),(0, 2, 0),(0, 0, 4)]` is a ______.
If A and B are symmetric matrices, then AB – BA is a ______.
If A is symmetric matrix, then B′AB is ______.
If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.
If A and B are any two matrices of the same order, then (AB)′ = A′B′.
If A and B are symmetric matrices of the same order, then ____________.
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 and B be and two 3 × 3 matrices. If A is symmetric and B is skewsymmetric, then the matrix AB – BA is ______.
If `[(2, 0),(5, 4)]` = P + Q, where P is symmetric, and Q is a skew-symmetric matrix, then Q 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 ______.
If A and B are symmetric matrices of the same order, then AB – BA is ______.
Which of the following is correct?
