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Determinant - Determinants of 2-by-2 matrices

Determinant - Determinants of 2-by-2 matrices: Encyclopedia II - Determinant - Determinants of 2-by-2 matrices

The 2×2 matrix has determinant . The interpretation when the matrix has real number entries is that this gives the area of the parallelogram with vertices at (0,0), (a,c), (b,d), and (a + b, c + d), with a sign factor (which is −1 if A as a transformation matrix flips the unit square o ...

Determinant: Encyclopedia II - Determinant - Determinants of 2-by-2 matrices

Determinant - Determinants of 2-by-2 matrices

The 2×2 matrix

has determinant

The interpretation when the matrix has real number entries is that this gives the area of the parallelogram with vertices at (0,0), (a,c), (b,d), and (a + b, c + d), with a sign factor (which is −1 if A as a transformation matrix flips the unit square over).

A formula for larger matrices will be given below.

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Adapted from the Wikipedia article "Determinants of 2-by-2 matrices", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki

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