Practice question · Fill in the blanks
Complete the classification.
If equals and both equal the number of unknowns, the system has a ______ solution; if the augmented rank is larger, the system is ______.
Word bank: unique · incompatible · trivial · homogeneous
Hints
- Matching ranks equal to the unknown count gives a single point.
- A rank jump in the augmented matrix signals a contradiction.
Show the answer
If equals and both equal the number of unknowns, the system has a unique solution; if the augmented rank is larger, the system is incompatible.
Why
Rouché–Frobenius in one sentence: matching full ranks = one point; a rank jump in the augmented matrix = contradiction.
Practise Systems of Linear Equations
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