I want to calculate the sum $a+b+c+d$ such that the following system has only the trivial solution. $$\begin{pmatrix} 0& 5& -9& -c\\ 1&0&0&-d\\5&0&-a&0\\5&9&-b&-9\\0&0&-5&-6\end{pmatrix}$$ I applied Gauss elimination algorithm and I got $$\begin{pmatrix} 1& 0& 0& -d\\ 0&1&-9/5&-c/5\\0&0&1&6/5\\0&0&0&-9+5d+9c/5-6/5(-b+81/5)\\0&0&0&5d+6/5a\end{pmatrix}$$ is this correct so far? how do we continue?
2026-03-28 05:01:03.1774674063
The system should have only trivial solution
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