Given $$ \det \begin{bmatrix} 7 & 1 & 4 \\ -2 & 3 & -1 \\ -1 & x & 0 \end{bmatrix} = 0 $$ Find a value for $x$.
My intial Idea was to let each of the lines equal to 0. Is this the right approach? I have worked down through it based on this but have hit the following sticking point.
So got this cleared up in the end. The question should be asking giving the determinant of the matrix given is equal to zero. Find x.
The wrong brackets are used. Should have been straight lines. Thanks to everyone for your input.
Answer I got
$$7\left[(3\times0) - (-1\times x)] -1[(-2\times0) - (-1\times(-1))] + 4[(-2\times x) - (3\times(-1))\right]$$
$$=7x -1 -8x + 12$$
$$=-x + 11~~(\text{= determinant})$$
$$∴ -x + 11 = 0$$
$$x = -11$$