2D Matrix Transformations
Change the numbers in a 2 × 2 matrix to see what happens to the grid.
Matrix
The first column is Ai. The second is Aj.
A =
Presets
Custom matrix.
Try a vector
Enter v = (x, y). The graph also shows Av.
det(A) = ad − bc
1.64
Area scale factor
1.64
Orientation
same
Vector transformation
(2, 1) → (3.90, 2)
Inverse
[[0.73, -0.43], [-0.24, 0.98]]
What the graph shows
Multiplying i = (1, 0) by A gives the first column of A. Multiplying j = (0, 1) by A gives the second column.
The white square has area 1. After multiplying by A, it becomes the coloured parallelogram. Its area is |det(A)|. A negative determinant means the grid has also been reflected.
det(A) = ad − bc
Area is multiplied by 1.64. Orientation stays the same.
If det(A) = 0, the parallelogram becomes a line or a point. A then has no inverse because more than one input can give the same output.