If $2x-3y+4z=0,5x-2y-z=0,21x-8y+az=0$ has infinitely many solutions, then |a| = 

$The condition for a homogeneous system to have infinitely many solutions is \Delta =0$

$\begin{array}{l}\Rightarrow \left|\begin{array}{ccc}2& -3& 4\\ 5& -2& -1\\ 21& -8& a\end{array}\right|=0\\ \Rightarrow 2\left(-2a-8\right)+3\left(5a+21\right)+4\left(-40+42\right)=0\\ \Rightarrow -4a-16+15a+63+8=0\end{array}$

$\begin{array}{l}\Rightarrow 11a+55=0\\ \Rightarrow 11a=-55\\ \Rightarrow a=-5\end{array}$