\(\begin{bmatrix} x & 1 & 0 \\ 1 & x & 1 \\ 0 & 1 & x \end{bmatrix}\) = 0 To find the value of x, we will have to calculate for the determined of the given matrix and equate it to 0 x[x\(^2\) - 1] - 1[x - 0] + 0[0 - 1] = 0 x\(^3\) - x] - x + 0 = 0 x\(^3\) - x - x = 0 x\(^3\) - 2x = 0 x\(^3\) = 2x x\(^2\) = 2 take the square root of both sides x = \(\sqrt{2}\)