# Math Help - Matrix: Find X, when Det=0

1. ## Matrix: Find X, when Det=0

Let

Then if ______

How would I begin to solve for X? Under what conditions does the determinant of the Matrix = 0.

2. For a 3X3 determinant:

$\begin{bmatrix}a&b&c\\d&e&f\\g&h&i\end{bmatrix}$

$a(ei-fh)-b(di-fg)+c(dh-eg)=0$

$=3(4(0)-(1)(5))-3(2x(0)-1(x))+1((2x)(5)-4x)=9x+15$

$9x+15=0$

$x=\frac{-5}{3}$