Determinants & Area

Drag the column vectors a₁ and a₂. Observe how crossing the vectors flips the orientation of the space, resulting in a negative determinant.

A =
2.00 2.00
1.00 2.00

Calculating | A |

| A | = ad − bc
= 2.00 × 2.00 − 1.00 × 2.00
= +2.00
Blue unit vector is to the left of the red one.
Blue transformed vector is to the
left of the red one.
The determinant is positive.

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