$$begin{cases} x + y + z = k \ ax + by + cz = |A| \ a^2x + b^2y + c^2z = |A|^2 end{cases}$$If $a, b,$ and $c$ are the distinct eigenvalues of $A$, determine the condition under which this system has a unique solution, and express that solution in te
$$begin{cases} x + y + z = k \ ax + by + cz = |A| \ a^2x + b^2y + c^2z = |A|^2 end{cases}$$If $a, b,$ and $c$ are the distinct eigenvalues of $A$, determine the condition under which this system has a unique solution, and express that solution in te
