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Proof: Matrix determinant gives area of image of unit square under mapping

Proof that the determinant of a 2X2 matrix gives the area of the image of the unit square under the mapping defined by the matrix. Created by Sal Khan.

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• what it means "unit square under mapping" ?
• A mapping is a function, or a transformation. They're all synonyms.

For a given point P in the domain, a function f(x) will send P to a particular point f(P) in the range. That point that it's mapped to is called the image of P, or the image of P under f.

Likewise for whole sets of points. If you have a set S of points in the domain, the set of points they're all mapped to is collectively called the image of S.

If you consider the set of points in a square of side length 1, the image of that set under a linear mapping will be a parallelogram. The title of the video says that if you find the matrix corresponding to that linear transformation, its determinant will be the area of that parallelogram.