Consider the system of linear equations (L):
\[
2x-y-z=-3,\qquad x+2y+z=4,\qquad 3x+y+kz=3
\]
Let \(k\in N\) and \(1\le k\le2026\). If
A={k:{ no solution}},
B={k:{ unique solution}},
C={k:{ infinite solutions}
then \(n(A)+n(B)+n(C)=\)}
Show Hint
For systems of linear equations, always compute the determinant first. If the determinant is non-zero, the system automatically has a unique solution and there is no need to check consistency conditions.