![]() Now we multiply the Adjugate by 1/Determinant to get:Ĭompare this answer with the one we got on Inverse of a Matrix Your Turn: try this for any other row or column, you should also get 10. Note: a small simplification is to multiply by the cofactors (which already have the "+−+−" pattern), and then we just add each time: This isn't too hard, because we already calculated the determinants of the smaller parts when we did "Matrix of Minors". Now find the determinant of the original matrix. ![]() in other words swap their positions over the diagonal (the diagonal stays the same): Now "Transpose" all elements of the previous matrix. In other words, we need to change the sign of alternate cells, like this: This is easy! Just apply a "checkerboard" of minuses to the "Matrix of Minors". Here are the first two, and last two, calculations of the " Matrix of Minors" (notice how I ignore the values in the current row and columns, and calculate the determinant using the remaining values):Īnd here is the calculation for the whole matrix: (It gets harder for a 3×3 matrix, etc) The Calculations For a 2×2 matrix (2 rows and 2 columns) the determinant is easy: ad-bc
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