Advertisements
Advertisements
प्रश्न
If the matrix `((6,-"x"^2),(2"x"-15 , 10))` is symmetric, find the value of x.
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
Matrix A = `[(0,2b,-2),(3,1,3),(3a,3,-1)]`is given to be symmetric, find values of a and b
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' = `[(-2,3),(1,2)] and B = [(-1,0),(1,2)]` then find (A + 2B)'
If A = `[(sin alpha, cos alpha), (-cos alpha, sin alpha)]` then verify that A'A = I
Find `1/2` (A + A') and `1/2` (A -A') When `A = [(0, a, b),(-a,0,c),(-b,-c,0)]`
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?
If A and B are symmetric matrices, then ABA is
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
Let A = `[(2, 3),(-1, 2)]`. Then show that A2 – 4A + 7I = O. Using this result calculate A5 also.
Show that A′A and AA′ are both symmetric matrices for any matrix A.
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.
Express the matrix `[(2, 3, 1),(1, -1, 2),(4, 1, 2)]` as the sum of a symmetric and a skew-symmetric matrix.
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 ______.
Sum of two skew-symmetric matrices is always ______ matrix.
If A and B are symmetric matrices, then BA – 2AB is a ______.
If A and B are any two matrices of the same order, then (AB)′ = A′B′.
AA′ is always a symmetric matrix for any matrix A.
If P is of order 2 x 3 and Q is of order 3 x 2, then PQ is of order ____________.
If A and B are symmetric matrices of the same order, then ____________.
The diagonal elements of a skew symmetric matrix are ____________.
Let A = `[(2, 3),(a, 0)]`, a ∈ R be written as P + Q where P is a symmetric matrix and Q is skew-symmetric matrix. If det(Q) = 9, then the modulus of the sum of all possible values of determinant of P is equal to ______.
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 ______.
Let A and B be and two 3 × 3 matrices. If A is symmetric and B is skewsymmetric, then the matrix AB – BA is ______.
If `[(2, 0),(5, 4)]` = P + Q, where P is symmetric, and Q is a skew-symmetric matrix, then Q is equal to ______.
If A and B are symmetric matrices of the same order, then AB – BA is ______.
