Unit 6: The determinant
About this unit
The determinant of a matrix is the factor its linear map multiplies every area (in 3D, every volume) by; a negative determinant means the space is flipped over, zero means it is flattened, and det(AB) = det(A)·det(B).
By the end, you can: See the determinant as the factor a linear map scales areas and volumes by, read its sign and its zero, and compute it for a 2×2 matrix.
Modules
5 modulesLearn
- How much area changesArticle · The determinant is the factor a linear map multiplies every area by: read it off the unit square's image. A negative sign means the plane is flipped; zero means it collapses onto a line or a point.Not started
- Where ad − bc comes fromArticle · For [[a, b], [0, d]] the parallelogram has base a and height d, so its area is ad; in general det = ad − bc. In 3D the determinant scales volumes, and det(AB) = det(A)·det(B).Not started
- Flip the parallelogramExperiment · Drag a column until det A = −2 and see that only the height above the other column matters, and that crossing it flips the sign.Not started
- The determinant in briefReview · What the determinant measures, what its sign and zero mean, how to compute it and how it behaves under products.Not started