QuestionCheck if the system has a nontrivial solution using minimal row operations:
$\begin{array}{r} 8 x_{1}-4 x_{2}+20 x_{3}=0 \\ -8 x_{1}-4 x_{2}-14 x_{3}=0 \\ 16 x_{1}+8 x_{2}+28 x_{3}=0 \end{array}$
Options: A. Impossible to determine. B. Nontrivial solution. C. Only trivial solution.

Studdy Solution
From the final matrix, we can see that the third equation is $0=0$ , which is always true. This means that the system is dependent and has an infinite number of solutions, including the nontrivial ones.
So, the system has a nontrivial solution.
The correct answer is B. The system has a nontrivial solution.

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