Visualizing cofactor expansion as signed volume decomposition
I made a visualization of cofactor expansion for a 3×3 determinant.
The idea is to start with the usual interpretation of det(A) as signed volume, then show each cofactor term as:
• one coordinate projection of the expansion column
• one projected 2×2 minor in the orthogonal coordinate plane
So instead of treating
det(A) = a₁₁M₁₁ − a₂₁M₂₁ + a₃₁M₃₁
as only a symbolic rule, the goal is to make the three terms look like signed volume pieces.
The image shows the three terms for one example matrix, including the “same sign / negated sign” behavior of the cofactor signs.
Full explanation, including determinant sign:
https://www.graphmath.com/la/determinant/determinant-sign.html
I would be interested in feedback on whether the geometric interpretation is clear
