This yields the system:
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- v_1 & v_2 & v_3 \\
- & 2 & 3 \\
- \end{vmatrix} = \langle 2v_3 - 3v_2, 3v_1 - v_3, v_2 - 2v_1 \rangle = \langle 4, 5, 6 \rangle.
- 2v_3 - 3v_2 = 4, \quad 3v_1 - v_3 = 5, \quad v_2 - 2v_1 = 6.
- From the third equation, $v_2 = 6 + 2v_1$. Substituting into the first equation:
- 2v_3 - 3(6 + 2v_1) = 4 \implies 2v_3 - 18 - 6v_1 = 4 \implies 2v_3 = 22 + 6v_1 \implies v_3 = 11 + 3v_1.
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