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Let $C$, $p_1,\ldots,p_n$ and $q_1,\ldots,q_n$ be positive real numbers. How solve this equation in general to end up with a general formula for each $x_k$? \begin{equation} \left(\begin{array}{cccccc} p_1 & p_2 & p_3 & \cdots & p_{n-1} & p_n \\ q_1 & -q_2 & 0 & \cdots & 0 & 0 \\ 0 & q_2 & -q_3 & \cdots & 0 & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\ 0 & 0 & 0 & \cdots & q_{n-1} & -q_n \end{array}\right) \left(\begin{array}{c} x_1 \\ \vdots \\ x_n \end{array}\right) = \left(\begin{array}{c} C \\ 0 \\ \vdots \\ 0 \end{array}\right) \end{equation}

hardy5
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1 Answers1

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If you move the top row to the bottom, the matrix is nearly in row echelon form.