For what value of $x$ is $\begin{bmatrix} 1 & x & 1 \end{bmatrix}\begin{bmatrix} 1 & 0 & 2 \\ 0 & 1 & 1 \\ 2 & 1 & 1 \end{bmatrix}\begin{bmatrix} 1 \\ 1 \\ x \end{bmatrix} = O$?

Explanation

1. 01

   First the row times the matrix: $\begin{bmatrix} 3 & x + 1 & x + 3 \end{bmatrix}$.

2. 02

   Then times the column: $3 + (x + 1) + x(x + 3) = x^2 + 4x + 4 = (x + 2)^2$.

3. 03

   $(x + 2)^2 = 0$ gives $x = -2$.