Advertisements
Advertisements
प्रश्न
Number of symmetric matrices of order 3 × 3 with each entry 1 or – 1 is ______.
पर्याय
512
64
8
4
Advertisements
उत्तर
Number of symmetric matrices of order 3 × 3 with each entry 1 or – 1 is 64.
Explanation:
Let us form a symmetric matrix of 3 × 3 order.
`[(a, b, c),(b, d, e),(c, e, f)]`
To fill a, b, c, d, e, f, we have 2 choices either 1 or – 1.
So, number of symmetric matrices will be 26 = 64.
APPEARS IN
संबंधित प्रश्न
If A' = `[(-2, 3),(1, 2)]` and B = `[(-1, 0),(1, 2)]`, then find (A + 2B)'
If A = `[(cos α, sin α), (-sin α, cos α)]`, then verify that A' A = I
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.
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)]`
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 \[A = \begin{bmatrix}1 & 2 \\ 0 & 3\end{bmatrix}\] is written as B + C, where B is a symmetric matrix and C is a skew-symmetric matrix, then B is equal to.
If A is a square matrix, then AA is a
If A and B are symmetric matrices, then ABA is
If A and B are matrices of the same order, then ABT − BAT is a
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)]`
Let A = `[(2, 3),(-1, 2)]`. Then show that A2 – 4A + 7I = O. Using this result calculate A5 also.
If A = `[(0, 1),(1, 1)]` and B = `[(0, -1),(1, 0)]`, show that (A + B)(A – B) ≠ A2 – B2
Show that A′A and AA′ are both symmetric matrices for any matrix 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 symmetric matrix, then A3 is a ______ matrix.
AA′ is always a symmetric matrix for any matrix A.
If A and B are symmetric matrices of the same order, then ____________.
If A and B are symmetric matrices of the same order, then ____________.
If A = `[(3, "x" - 1),(2"x" + 3, "x" + 2)]` is a symmetric matrix, then x = ____________.
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 ____________.
If A = [aij] is a skew-symmetric matrix of order n, then ______.
