Stewart Malone
09/26/2024 · High School
1. Solve the following system of linear equations using the Gauss elimination method: \[ \begin{aligned} x+y+2 z=9 \\ 2 x+4 y-3 z=1 \\ 3 x+6 y-5 z=0\end{aligned} \] \[ \begin{array}{l}x=1 \\ y=2 \\ 2\end{array} \] 2. Find a root of the equation \( \mathrm{f}(\mathrm{x})=2 e^{2 x}-5 \) using the Newton-Raphson method. Use an initial guess of \( x_{0}=1 \) and perform three iterations to approximate the root. Round your answers to four decimal places. (8 Marks)
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1. The solution to the system of linear equations is \(x = 1\), \(y = 2\), and \(z = 3\).
2. The approximate root of the equation \(f(x) = 2e^{2x} - 5\) using the Newton-Raphson method with three iterations is \(x \approx 0.4600\).
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