Practice question · Sort into groups
Sort these into properties of Invertible or Singular matrices.
Groups: Invertible · Singular
- Has a zero eigenvalue
- has only the trivial solution
- The rows span
- rank(A) < n
- ≠ 0
Hints
- Sort by whether each property survives when the determinant vanishes.
- Full rank and a trivial null space go together.
Show the answer
Invertible: ≠ 0, The rows span , has only the trivial solution
Singular: Has a zero eigenvalue, rank(A) < n
Why
The Invertible Matrix Theorem gives many equivalent conditions.
Practise Problem-Solving: Linear Algebra
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