Practice question · Multiple choice
A matrix has determinant 10⁻¹⁸ in double precision. Is it singular?
Hints
- Multiply a 10×10 matrix by 0.1. What happens to its determinant?
- Ask whether 'close to zero' means the same thing for matrices of different magnitudes.
Show the answer
A. Unanswerable alone, since the determinant scales with the matrix
Why
Scaling a 10×10 matrix by 0.1 multiplies its determinant by 10⁻¹⁰ without changing its invertibility at all, so the number carries no scale-free information. The condition number is the right instrument, and it also tells you how many digits of the answer to trust.
Practise Determinants and Invertibility
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