What is meant by the determinant of a matrix?
Assuming that we have a square matrix, then the determinant of the matrix is the determinant with the same elements.
Eg if we have a
# bb(A) = ( (a,b), (c,d) ) #
The the associated determinant given by
# D = | bb(A) | = | (a,b), (c,d) | = ad-bc#
To extend on Steve's explanation, the determinant of a matrix tells you whether or not the matrix is invertible. If the determinant is 0, the matrix is not invertible.
For example, let
If we let
Additionally, the determinant is involved in computing the inverse of a matrix. Given a matrix
Also area / volume scale factor...
The determinant is also used as a area/volume scale factor,
If we have a
Then if a particular shape of area