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Solve the following.
If the matrix (6 -x²; 2x - 15 10) is symmetric, find the value of x.
If the matrix $\begin{pmatrix} 6 & -x^2 \\ 2x - 15 & 10 \end{pmatrix}$ is symmetric, find the value of $x$.
Answer
Answer
A matrix is symmetric when $a_{12} = a_{21}$.
$-x^2 = 2x - 15$
$x^2 + 2x - 15 = 0$
$(x + 5)(x - 3) = 0$
Hence $x = 3$ or $x = -5$.
Final answer: $x = 3$ or $x = -5$