(a) Determine $a$ and $b$ so that the system. $$ x+y+z=6, x+2 y+3 z=12, x+3 y+a z=b, $$ has (i) No solution (ii) Unique solution (iii) Infinite solution.
Explanation
The system of equations is represented in the form $AX=B$. The given conditions are used to determine the values of $a$ and $b$ for which the system has no solution, unique solution, or infinite solution.
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