If the determinant = 0, this means...?

Question

If the determinant = 0, this means...?

Answer 1

If you can solve it, it means that it has got the same number of colums and rows. It comes from a matrix mxn and m=n.

If you are dealing with 2x2 dimension matrix, it means that

(a,b)=µ(c,d)

A number called µ exists and both vectors have got the same direction and sense though not the same length. We can only define a line with one vector or two points.

Using a bit of logic we can do it for three vectors.

If you´re dealing with 3x3 matrix, it means that

(a,b,c)=µ(d,e,f)+ß(g,h,i)

which says that one vector is correlated to the other two. Here we can define a plane or a flat surface or field using two vectors in the space.

Answer 2

The matrix is singular and not of full rank.

Answer 3

If the determinant is zero this means matrix is singular and the solution set of the equations which form the matrix can not be obtain.