If \begin{bmatrix}x&1&1\end{bmatrix}\begin{bmatrix}1&2&3\\ 4&5&6\\ 7&8&9\end{bmatrix}\begin{bmatrix}1\\ 1\\ x\end{bmatrix}= then which one of the following is a value of x?

Explanation

Multiply the first two matrices: \begin{bmatrix}x+4+7 & 2x+5+8 & 3x+6+9\end{bmatrix} = \begin{bmatrix}x+11 & 2x+13 & 3x+15\end{bmatrix}. Now multiply by the column vector: (x+11) + (2x+13) + x(3x+15) = 3x^2 + 18x + 24. Equating to 45 gives 3x^2 + 18x - 21 = 0 \implies x^2 + 6x - 7 = 0. The roots are x=1, -7.

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