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= `((3,5),(7,9))`is written as A = P + Q, where P is a symmetric matrix and Q is skew symmetric matrix, then write the matrix P.
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' = `[(3, 4),(-1, 2),(0, 1)]` and B = `[(-1, 2, 1),(1, 2, 3)]`, then verify that (A + B)' = A' + B'
If A' = `[(3, 4),(-1, 2),(0, 1)]` and B = `[(-1, 2, 1),(1, 2, 3)]`, then verify that (A – B)' = A' – B'
Show that the matrix A = `[(0, 1, -1),(-1, 0, 1),(1, -1, 0)]` 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.
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.
The matrix \[\begin{bmatrix}0 & 5 & - 7 \\ - 5 & 0 & 11 \\ 7 & - 11 & 0\end{bmatrix}\] is
Show that a matrix which is both symmetric and skew symmetric is a zero matrix.
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)]`
If A and B are symmetric matrices of the same order, then (AB′ –BA′) is a ______.
If A = `[(0, 1),(1, 1)]` and B = `[(0, -1),(1, 0)]`, show that (A + B)(A – B) ≠ A2 – B2
Sum of two skew-symmetric matrices is always ______ matrix.
If A and B are symmetric matrices, then BA – 2AB is a ______.
If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.
If A is any square matrix, then which of the following is skew-symmetric?
Number of symmetric matrices of order 3 × 3 with each entry 1 or – 1 is ______.
