What is the determinant of a matrix used for?

1 Answer
Shura
Jun 1, 2015

The determinant of a matrix A helps you to find the inverse matrix A^(-1).

You can know a few things with it :

  • A is invertible if and only if Det(A) != 0.

  • Det(A^(-1)) = 1/(Det(A))

  • A^(-1) = 1/(Det(A)) * ""^t((-1)^(i+j)*M_(ij)),

where t means the transpose matrix of ((-1)^(i+j)*M_(ij)),

where i is the n° of the line, j is the n° of the column of A,

where (-1)^(i+j) is the cofactor in the i-th row and j-th column of A,

and where M_(ij) is the minor in the i-th row and j-th column of A.

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