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ben committed 2026-10-07 08:52:59 -07:00
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College/AU 26/MATH 208 (Matrix Algebra)/Chapter 1.2 Notes.md
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@@ -41,3 +41,5 @@ h & 2h & \frac{2h}{3} \\ 0 & 12 - 2h & k - \frac{2h}{3}
\end{array}\right] $$ \end{array}\right] $$
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). 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 $$\begin{gather} 12-2h = 0 \\[1.5ex] h=6 \end{gather}$$ and $$ \begin{gather} k-\frac{2h}{3} \ne 0 \\[1.5ex] k-4 \ne 0 \\[1.5ex] k \ne 4 \end{gather}$$ This means that there are no solutions when $$\begin{gather} 12-2h = 0 \\[1.5ex] h=6 \end{gather}$$ and $$ \begin{gather} k-\frac{2h}{3} \ne 0 \\[1.5ex] k-4 \ne 0 \\[1.5ex] k \ne 4 \end{gather}$$