Advertisements
Advertisements
प्रश्न
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)]`
उत्तर
We have A = `[(2, 4, -6),(7, 3, 5),(1, -2, 4)]`
Then A' = `[(2, 7, 1),(4, 3, -2),(-6, 5, 4)]`
Hence `("A" + "A'")/2 = 1/2 [(4, 11, -5),(11, 6, 3),(-5, 3, 8)]`
= `[(2, 11/2, (-5)/2),(11/2, 3, 3/2),((-5)/2, 3/2, 4)]`
and `("A" - "A'")/2 = 1/2 [(0, -3, -7),(3, 0, 7/2),(7, -7, 0)]`
= `[(0, (-3)/2, (-7)/2),(3/2, 0, 7/2),(7/2, (-7)/2, 0)]`
Therefore,
`("A" + "A'")/2 + ("A" - "A'")/2 = [(2, 11/2, (-5)/2),(11/2, 3, 3/2),((-5)/2, 3/2, 4)] + [(0, (-3)/2, (-7)/2),(3/2, 0, 7/2),(7/2, (-7)/2, 0)]`
= `[(2, 4, -6),(7, 3,5),(1,-2, 4)]`
= A
APPEARS IN
संबंधित प्रश्न
if `A' [(3,4),(-1, 2),(0,1)] and B = [((-1,2,1),(1,2,3))]` then verify that (A - B)' = A' - B'
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]`
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.
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:
`[(1,5),(-1,2)]`
Show that all the diagonal elements of a skew symmetric matrix are zero.
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 and B are two matrices of order 3 × m and 3 × n respectively and m = n, then the order of 5A − 2B 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
Let A = `[(2, 3),(-1, 2)]`. Then show that A2 – 4A + 7I = O. Using this result calculate A5 also.
The matrix `[(1, 0, 0),(0, 2, 0),(0, 0, 4)]` is a ______.
The matrix `[(0, -5, 8),(5, 0, 12),(-8, -12, 0)]` is a ______.
If A and B are matrices of same order, then (AB′ – BA′) is a ______.
Sum of two skew-symmetric matrices is always ______ matrix.
If A is a skew-symmetric matrix, then A2 is a ______.
If A = `[(3, "x" - 1),(2"x" + 3, "x" + 2)]` is a symmetric matrix, then x = ____________.
If A, B are Symmetric matrices of same order, then AB – BA is a
If A = [aij] is a skew-symmetric matrix of order n, 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 ______.
If `[(2, 0),(5, 4)]` = P + Q, where P is symmetric, and Q is a skew-symmetric matrix, then Q is equal to ______.
Number of symmetric matrices of order 3 × 3 with each entry 1 or – 1 is ______.
