Advertisements
Advertisements
Question
If the matrix `((6,-"x"^2),(2"x"-15 , 10))` is symmetric, find the value of x.
Advertisements
Solution
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
RELATED QUESTIONS
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 = `[(cos α, sin α), (-sin α, cos α)]`, then verify that A' A = I
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
`[(3, 5),(1, -1)]`
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
`[(1, 5),(-1, 2)]`
If A and B are symmetric matrices, prove that AB – BA is a skew symmetric matrix.
If the matrix A is both symmetric and skew symmetric, then ______.
Write a square matrix which is both symmetric as well as skew-symmetric.
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?
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.
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.
______ matrix is both symmetric and skew-symmetric matrix.
Sum of two skew-symmetric matrices is always ______ matrix.
If A is a symmetric matrix, then A3 is a ______ matrix.
If A and B are any two matrices of the same order, then (AB)′ = A′B′.
Which of the following is correct?
For a skew-symmetric matrix \[A=[a_{ij}]_{n\times n}\], which relation holds for all \[i\] and \[j\]?
Which expression writes any square matrix \[A\] as the sum of a symmetric and a skew-symmetric matrix?
Why does multiplying \[A+A^T\] by \[\frac{1}{2}\] not change its symmetric property?
