Question 3.3.5: The computation in Example 2 (disregarding the fourth column...

The computation in Example 2 (disregarding the fourth column in each matrix there) shows that the matrix

A =  \left [\begin{matrix} 1 & 2 & 1 \\ 3 & 8 & 7 \\ 2 & 7 & 9 \end{matrix}\right ]

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is row equivalent to the 3 × 3 identity matrix. Hence Theorem 4 implies that the homogeneous system

x_{1} + 2 x_{2} + x_{3} = 0

3 x_{1} + 8 x_{2} + 7 x_{3} = 0

2 x_{1} + 7 x_{2} + 9 x_{3} = 0

with coefficient matrix A has only the trivial solution x_{1} = x_{2} = x_{3} = 0.

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