Given: The system of equations 2x+y−3z=5 3x−2y+2z=5 and 5x−3y−z=16 So, A=[
2
1
−3
3
−2
2
5
−3
−1
] det(A)=|A|=2×{(−2×−1)−(−3×2)}−1×{(3×−1)−(2×5)}+(−3)×{(3×−3)−(5×−2)} ⇒|A|=2×(2+6)−1×(−3−10)−3×(−9+10) ⇒|A|=16+13−3=26 ∴|A|≠0 So, system is consistent having unique solution.