Practice question · Select all that apply
A system in 4 unknowns reduces to 3 pivots with no inconsistent row. Select every TRUE statement.
Hints
- Rank is the pivot count; free variables are unknowns minus rank.
- Any free variable at all rules out uniqueness.
Show the answer
- C. The rank is 3
- D. The system has infinitely many solutions
- E. There is exactly 1 free variable
Why
3 pivots means rank 3, so 4 - 3 = 1 free variable, and one free parameter already produces infinitely many solutions. Uniqueness would need 4 pivots, and inconsistency was ruled out by hypothesis. Rank alone settles all three questions.
Practise Gaussian Elimination and Rank
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