Practice question · Fill in the blanks
Complete the fundamental equivalence.
A square matrix is invertible exactly when its determinant is ______; geometrically, a zero determinant means the unit square collapses to a ______.
Word bank: nonzero · line · positive · circle
Hints
- A nonzero value corresponds to invertibility.
- A vanishing value means the transformation collapses the space.
Show the answer
A square matrix is invertible exactly when its determinant is nonzero; geometrically, a zero determinant means the unit square collapses to a line.
Why
Nonzero determinant ⟺ invertible; zero ⟺ collapse to a line (or point), the algebra and the geometry of the same fact.
Practise Determinants
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