Lesson 30 of 48
Systems, determinants, rank
When a system has one solution, none, or infinitely many — and why.
A zero determinant is not a computational curiosity; it means the transformation squashed space flat, and squashing loses information you cannot get back. That is the same reason some models are unidentifiable.
Do this
Solve a 3×3 system by elimination, by hand, showing every row operation. Then deliberately build a system with no unique solution and compute its determinant.
The question that unlocks the next lesson
A square system's matrix has determinant 0. What follows?
- AThere is exactly one solution
- BThere is no unique solution — either none or infinitely many
- CAll variables must be zero
- DThe system is always inconsistent