vault backup: 2026-10-05 09:39:55

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ben committed 2026-10-05 09:39:55 -07:00
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commit a5ec51b203
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+1 -4
@@ -40,7 +40,4 @@ h & 2h & \frac{2h}{3} \\ h & 12 & k
h & 2h & \frac{2h}{3} \\ 0 & 12 - 2h & k - \frac{2h}{3}
\end{array}\right] $$
There are no solutions the system of equations when there is no pivot in a row and the value on the right is not equal to zero (if the value on the right is also equal to zero than that equation is essentially $0=0$ which is always true).
This means that there are no solutions when $$12-2h = 0 \to h=6$$ and $$ \begin{gather} k-\frac{2h}{3} \ne 0 \\ k-4 \ne 0 \\[1.5ex] k \ne 4 \end{gather}$$
This means that there are no solutions when $$\begin{gather} 12-2h = 0 \\[1.5ex] h=6 \end{gather}$$ and $$ \begin{gather} k-\frac{2h}{3} \ne 0 \\[1.5ex] k-4 \ne 0 \\[1.5ex] k \ne 4 \end{gather}$$