1. **Problem:** Solve the system of equations using two iterations of Jacobi's iteration method: $$\begin{cases} 10x + y + z = 12 \\ x + 10y + z = 13 \\ x + y + 10z = 14 \end{cases}$$ 2. **Jacobi's iteration formula:** For each variable, isolate it: $$x^{(k+1)} = \frac{1}{10}(12 - y^{(k)} - z^{(k)})$$ $$y^{(k+1)} = \frac{1}{10}(13 - x^{(k)} - z^{(k)})$$ $$z^{(k+1)} = \frac{1}{10}(14 - x^{(k)} - y^{(k)})$$ 3. **Initial guess:** Start with $x^{(0)}=0$, $y^{(0)}=0$, $z^{(0)}=0$. 4. **First iteration ($k=0$ to $k=1$):** $$x^{(1)} = \frac{1}{10}(12 - 0 - 0) = 1.2$$ $$y^{(1)} = \frac{1}{10}(13 - 0 - 0) = 1.3$$ $$z^{(1)} = \frac{1}{10}(14 - 0 - 0) = 1.4$$ 5. **Second iteration ($k=1$ to $k=2$):** $$x^{(2)} = \frac{1}{10}(12 - y^{(1)} - z^{(1)}) = \frac{1}{10}(12 - 1.3 - 1.4) = \frac{1}{10}(9.3) = 0.93$$ $$y^{(2)} = \frac{1}{10}(13 - x^{(1)} - z^{(1)}) = \frac{1}{10}(13 - 1.2 - 1.4) = \frac{1}{10}(10.4) = 1.04$$ $$z^{(2)} = \frac{1}{10}(14 - x^{(1)} - y^{(1)}) = \frac{1}{10}(14 - 1.2 - 1.3) = \frac{1}{10}(11.5) = 1.15$$ 6. **Result after two iterations:** $$(x, y, z) = (0.93, 1.04, 1.15)$$ 7. **Answer choice:** (d) (0.93, 1.04, 1.15)