10/29/2023 0 Comments Computing adjoint of a matrixIs it the same? Which method do you prefer? Larger Matrices 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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