All simulators
A Matrix as a Transformation
Edit a 2×2 matrix and see the plane stretch, rotate, shear or collapse; the determinant is the area of the image square.
Day 17: Matrix Multiplication, Transpose & the Design Matrixdet A
-5.00
flips orientation
Ax
(3.0, 4.0)
= 1·col₁ + 1·col₂
The faint grid is the original plane; the coloured grid is its image under A. The unit square (grey) becomes the parallelogram spanned by the columns Aî and Aĵ, with area |det A|. Drag x (blue) to see Ax (orange).