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Define the \\( 100 \\times 100 \\) square matrix \\( A \\) and the column vector \\( b \\) by \\[ A_{i j}=I_{i j}+\\frac{1}{-j^{2}+2}, b_{i}=1+\\frac{1}{i}, 1 \\leq i, j \\leq 100 \\] where \\( I_{i j} \\) is the \\( 100 \\times 100 \\) identity matrix (i.e. 1 on the main diagonal and 0 everywhere else). Solve \\( A x=b \\) for \\( x \\) using both the Gauss-Seidel method and the \\( A \\backslash b \\) construct. Do not give the whole vector \\( x \\) in your output, but only \\( x_{2}, x_{50} \\) and \\( x_{99} \\). [20] Define the \\( 100 \\times 100 \\) square matrix \\( A \\) and the column vector \\( b \\) by \\[ A_{i j}=I_{i j}+\\frac{1}{-j^{2}+2}, b_{i}=1+\\frac{1}{i}, 1 \\leq i, j \\leq 100 \\] where \\( I_{i j} \\) is the \\( 100 \\times 100 \\) identity matrix (i.e. 1 on the main diagonal and 0 everywhere else). Solve \\( A x=b \\) for \\( x \\) using both the Gauss-Seidel method and the \\( A \\backslash b \\) construct. Do not give the whole vector \\( x \\) in your output, but only \\( x_{2}, x_{50} \\) and \\( x_{99} \\). [20]