1. **Problem Statement:** Determine if the given system of linear equations is strictly diagonally dominant and identify the correct sequence. The system is: (i) $x - 2y + 52 = 8$ (ii) $5x + 8y - 22 = 10$ (iii) $3x - y - 2 = 2$ 2. **Definition:** A system is strictly diagonally dominant if for each equation, the absolute value of the coefficient of the variable on the diagonal is greater than the sum of the absolute values of the other coefficients in that equation. 3. **Rewrite equations in standard form:** (i) $x - 2y = 8 - 52 \Rightarrow x - 2y = -44$ (ii) $5x + 8y = 10 + 22 \Rightarrow 5x + 8y = 32$ (iii) $3x - y = 2 + 2 \Rightarrow 3x - y = 4$ 4. **Check diagonal dominance for each equation:** - Equation (i): diagonal coefficient is $1$ (for $x$), sum of other coefficients is $| -2 | = 2$. Since $1 \not> 2$, not strictly diagonally dominant. - Equation (ii): diagonal coefficient is $8$ (for $y$), sum of other coefficients is $|5| = 5$. Since $8 > 5$, strictly diagonally dominant. - Equation (iii): diagonal coefficient is $-1$ (for $y$), sum of other coefficients is $|3| = 3$. Since $1 \not> 3$, not strictly diagonally dominant. 5. **Check if rearranging equations can make the system strictly diagonally dominant:** Try sequence (ii), (i), (iii): - (ii): diagonal $8$, sum others $5$, $8 > 5$ ✓ - (i): diagonal $1$, sum others $2$, $1 \not> 2$ ✗ - (iii): diagonal $-1$, sum others $3$, $1 \not> 3$ ✗ Try sequence (ii), (iii), (i): - (ii): diagonal $8$, sum others $5$, $8 > 5$ ✓ - (iii): diagonal $-1$, sum others $3$, $1 \not> 3$ ✗ - (i): diagonal $1$, sum others $2$, $1 \not> 2$ ✗ Try sequence (i), (iii), (ii): - (i): diagonal $1$, sum others $2$, $1 \not> 2$ ✗ - (iii): diagonal $-1$, sum others $3$, $1 \not> 3$ ✗ - (ii): diagonal $8$, sum others $5$, $8 > 5$ ✓ Try sequence (i), (ii), (iii): - (i): diagonal $1$, sum others $2$, $1 \not> 2$ ✗ - (ii): diagonal $8$, sum others $5$, $8 > 5$ ✓ - (iii): diagonal $-1$, sum others $3$, $1 \not> 3$ ✗ 6. **Conclusion:** Only equation (ii) is strictly diagonally dominant in any sequence. None of the sequences make the entire system strictly diagonally dominant. **Final answer:** None of the sequences (a, b, c, d) make the system strictly diagonally dominant. --- **Note:** Since the user asked to solve all but per instructions only the first problem is solved here.