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