Apply the Gauss-Seidel method to the given system. Take the zero vector as the initial approximation and work with four-significant-digit accuracy until two successive iterates agree within 0.001 in each variable. (Round your answers to three decimal places.) 7x1 - x2 = 4 x1 - 5x2 = -14 x1 = x2 = Compare the number of iterations required by the Jacobi and Gauss-Seidel methods to reach such an approximate solution. The Jacobi method requires more iteration(s) than the Gauss-Seidel method.
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Write down the given system of linear equations: \[ \begin{cases} a_{11}x_1 + a_{12}x_2 + \cdots + a_{1n}x_n = b_1 \\ a_{21}x_1 + a_{22}x_2 + \cdots + a_{2n}x_n = b_2 \\ \vdots \\ a_{n1}x_1 + a_{n2}x_2 + \cdots + a_{nn}x_n = b_n \end{cases} Show more…
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