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Please give an easy explanation, high school level.

GoodDeeds
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jijl
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  • Welcome to math. SE. Have you searched on the web before posting this question ? – Shailesh Apr 25 '16 at 09:34
  • Yes. But still don't understand – jijl Apr 25 '16 at 09:37
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    What are $a$ and $b$? – GoodDeeds Apr 25 '16 at 09:37
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    see: http://math.stackexchange.com/questions/29128/why-determinant-of-a-2-by-2-matrix-is-the-area-of-a-parallelogram – Emilio Novati Apr 25 '16 at 09:39
  • The link of Emilio Novati contains a beautiful solution. Another (lenghty but conceptually easy) solution is described here: https://www.khanacademy.org/math/linear-algebra/matrix_transformations/determinant_depth/v/linear-algebra-determinant-and-area-of-a-parallelogram – Darío G Apr 25 '16 at 09:44
  • That the determinant of a $2 \times 2$ matrix is the signed area of the parallelogram generated by the columns of the matrix ought to be the definition of the determinant. Then the question changes to: how does the usual formula for the determinant follow from this definition? This is an exercise in cutting a parallelogram into triangles. – Dan Fox Apr 25 '16 at 10:11

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