Advertisements
Advertisements
प्रश्न
If the matrix `((6,-"x"^2),(2"x"-15 , 10))` is symmetric, find the value of x.
Advertisements
उत्तर
Let A = `[(6,-"x"^2),(2"x" - 15, 10)]`
A' = `[(6,2"x"-15),(-"x"^2,10)]`
Since given matrix A is symmetric
∴ A = A'
`[(6,-"x"^2),(2"x" -15,10)] = [(6,2"x"-15),(-"x"^2,10)]`
Equating the corresponding terms of equal matrices, we obtain.
2x - 15 = - x2
⇒ x2 + 2x - 15 = 0
⇒ (x+5)(x-3)=0
⇒ x = -5 and x = 3
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'
For the matrices A and B, verify that (AB)′ = B'A' where A = `[(0),(1),(2)]`, B = `[(1, 5, 7)]`
If A = `[(sin α, cos α), (-cos α, sin α)]`, then verify that A'A = I
Show that the matrix B'AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.
If the matrix A is both symmetric and skew symmetric, then ______.
If A and B are symmetric matrices of the same order, write whether AB − BA is symmetric or skew-symmetric or neither of the two.
Write a square matrix which is both symmetric as well as skew-symmetric.
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 \[A = \begin{bmatrix}2 & 0 & - 3 \\ 4 & 3 & 1 \\ - 5 & 7 & 2\end{bmatrix}\] 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
If A and B are matrices of the same order, then ABT − BAT is a
If A and B are two skew-symmetric matrices of same order, then AB is symmetric matrix if ______.
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.
If A and B are matrices of same order, then (AB′ – BA′) is a ______.
If A and B are symmetric matrices, then AB – BA is a ______.
AA′ is always a symmetric matrix for any matrix A.
Number of symmetric matrices of order 3 × 3 with each entry 1 or – 1 is ______.
For the matrices \[P=\frac{1}{2}(B+B^T)\] and \[Q=\frac{1}{2}(B-B^T)\], what is \[P+Q\]?
