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Home » $ \sum t_i t_j = 7 $ - Treasure Valley Movers

$ \sum t_i t_j = 7 $ - Treasure Valley Movers

📅 April 15, 2026 👤 scraface

Apr 15, 2026

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📌 From the third equation: $x = 1 - 2y$.

📌 2z - 4(1 - 2y) = -6 \Rightarrow 2z - 4 + 8y = -6 \Rightarrow 2z + 8y = -2 \Rightarrow z + 4y = -1

📌 Now solve the first and new second equation:

📌 z + 4y = -1

📌 \Rightarrow \text{Subtract: } 0 = 6 \Rightarrow \text{Contradiction}

📌 This suggests no solution exists unless the given cross product is inconsistent with the vector.

📌 However, cross product outputs are orthogonal to $\mathbf{a}$. Check:

📌 \begin{pmatrix} 5 \\ -6 \\ -1 \end{pmatrix} \cdot \begin{pmatrix} 2 \\ -1 \\ 4 \end{pmatrix} = 10 + 6 - 4 = 12 \ne 0

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