Advertisements
Advertisements
Question
if `A' [(3,4),(-1, 2),(0,1)] and B = [((-1,2,1),(1,2,3))]` then verify that (A - B)' = A' - B'
Advertisements
Solution
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
RELATED QUESTIONS
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'
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'
Show that the matrix A = `[(1,-1,5),(-1,2,1),(5,1,3)]` is a 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)]`
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.
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 is a square matrix, then AA is a
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 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 \[A = \begin{bmatrix}0 & - 5 & 8 \\ 5 & 0 & 12 \\ - 8 & - 12 & 0\end{bmatrix}\] is a
The matrix \[A = \begin{bmatrix}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{bmatrix}\] is
If the matrix `((6,-"x"^2),(2"x"-15 , 10))` is symmetric, find the value of x.
If A = `[(0, 1),(1, 1)]` and B = `[(0, -1),(1, 0)]`, show that (A + B)(A – B) ≠ A2 – B2
If A = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, and A–1 = A′, find value of α
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 is a skew-symmetric matrix, then A2 is a ______.
If A and B are symmetric matrices, then AB – BA is a ______.
If A is symmetric matrix, then B′AB is ______.
If A and B are any two matrices of the same order, then (AB)′ = A′B′.
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 ____________.
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 ______.
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?
