Practice question · Multiple choice
A determinant of zero is often described as 'no unique solution'. What is the geometric fact behind that phrase?
Hints
- The determinant measures how the transformation scales area. What does a factor of zero do?
- Ask whether a squashed image can be un-squashed.
Show the answer
D. The matrix collapses space onto a lower dimension
Why
Zero determinant means the transformation flattens the space, and flattening destroys the information you would need to reverse it. Option 3 is one possible consequence but not the meaning, a singular system may have infinitely many solutions rather than none.
Practise Determinants
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More questions on Determinants
- A transformation matrix has det A = 3. A region of area 8 goes in. Set the slider to the area that comes out.
- Complete the fundamental equivalence.
- Compute detbeginpmatrix 5 & 3 4 & 2 endpmatrix.
- Sort each fact by what it does to a determinant.
- Match each statement to its equivalent.
- An economist’s two policy instruments act on two targets through matrix A, and det A = 0. What does this mean…