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
We know that, `"A" = [(3, -1, 0),(4,2,1)]` and B' = `[(-1,1),(2,2),(1,3)]`
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)]`
`= [(4, -3,-1),(3, 0,-2)]`
so, (A - B)' = `[(4,3),(-3,0),(-1,-2)]` ..... (i)
Then, 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)]`
`= [(4,3),(-3,0),(-1,-2)]` ..... (ii)
Equations (i) and (ii) prove that,
(A - B)' = A' - B'
APPEARS IN
संबंधित प्रश्न
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'
if `A' [(3,4),(-1, 2),(0,1)] and B = [((-1,2,1),(1,2,3))]` 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]`
For the matrices A and B, verify that (AB)′ = B'A' where `A =[(0), (1),(2)] , B =[1 , 5, 7]`
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)]`
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.
Show that all the diagonal elements of a skew symmetric matrix are zero.
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.
For what value of x, is the matrix \[A = \begin{bmatrix}0 & 1 & - 2 \\ - 1 & 0 & 3 \\ x & - 3 & 0\end{bmatrix}\] a skew-symmetric matrix?
If a matrix A is both symmetric and skew-symmetric, then
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 \[A = \begin{bmatrix}2 & 0 & - 3 \\ 4 & 3 & 1 \\ - 5 & 7 & 2\end{bmatrix}\] is expressed as the sum of a symmetric and skew-symmetric matrix, then the symmetric matrix is
If A and B are two matrices of order 3 × m and 3 × n respectively and m = n, then the order of 5A − 2B is
The matrix \[A = \begin{bmatrix}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{bmatrix}\] is
Express the matrix A as the sum of a symmetric and a skew-symmetric matrix, where A = `[(2, 4, -6),(7, 3, 5),(1, -2, 4)]`
If A and B are two skew-symmetric matrices of same order, then AB is symmetric matrix if ______.
If A = `[(0, 1),(1, 1)]` and B = `[(0, -1),(1, 0)]`, show that (A + B)(A – B) ≠ A2 – B2
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.
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 and B are symmetric matrices, then BA – 2AB is a ______.
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 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 ____________.
The diagonal elements of a skew symmetric matrix are ____________.
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 `[(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 ______.
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 ______.
