The linear system x₁ − x₃ = 0.2, −1/2 x₁ + x₂ – 1/4 x₃ = −1.425, x₁ – 1/2 x₂ + x₃ = 2. Has the solution (0.9,−0.8, 0.7)^t .

a. Is the coefficient matrix

Strictly diagonally dominant?

b. Compute the spectral radius of the Gauss-Seidel matrix T_g.

c. Use the Gauss-Seidel iterative method to approximate the solution to the linear system with a tolerance of 10⁻² and a maximum of 300 iterations.

d. What happens in part (c) when the system is changed to x₁ − 2x₃ = 0.2, −1/2 x₁ + x₂ – 1/4 x₃ = −1.425, x₁ – 1/2 x₂ + x₃ = 2.

1 -4 A = 1 1