Difference between revisions of "Adjugate Formula"
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The adjugate formula defines the inverse of an n-by-n square matrix <math>\mathbf{A}</math> as<br/><br/> | The adjugate formula defines the inverse of an n-by-n square matrix <math>\mathbf{A}</math> as<br/><br/> |
Revision as of 10:16, 12 May 2014
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The adjugate formula defines the inverse of an n-by-n square matrix as
where is the so called adjugate matrix of . The adjugate matrix is the transposed of the cofactor matrix:
And the cofactor matrix is just a matrix where each cell corresponds to the related cofactor:
So to determine the inverse of an n-by-n square matrix you have to compute the n square cofactors, then transpose the resulting cofactor matrix and divide all the values by the determinant.
Example: inverse of a 4-by-4 matrix using the adjugate formula
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