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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