Lane Park
10/19/2023 · Junior High School
(30 points) Solve the system of linear equations using Ganss-Jordan method. Find the rank of the matrix of this system. Indicate dependent and independent uariables. Find the fundamental solution set (write the answer as a linear combination of particular vectors) \[ \left\{\begin{array}{l}-2 x_{1}+x_{2}+8 x_{3}=0 \\ 7 x_{1}-2 x_{2}-22 x_{3}=0 \\ 3 x_{1}-x_{2}-10 x_{3}=0\end{array}\right. \]
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The system's solution is \( x_1 = \frac{26}{7}x_3 \) and \( x_2 = 2x_3 \). The rank is 2, with \( x_3 \) as the independent variable. The fundamental solution set is \( \begin{pmatrix} \frac{26}{7} \\ 2 \\ 1 \end{pmatrix}x_3 \).
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