Question

If the matrix `((6,-"x"^2),(2"x"-15 , 10))` is symmetric, find the value of x.

Answer 1

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