Question

I know how to find the determinant of a matrix. However I dont know what this number is used for; or what is the physical meaning of it. Can someone explain it? Thanks

Answer 1

It seems you know already that determinant can be used to compute area of triangles. Here is another application: http://www.math.ucdavis.edu/~daddel/linear_algebra_appl/Applications/Determinant/Determinant/node11.html
The role of determinant is similar to the discriminant of a quadratic equation. The determinant tells us if Ax=0 has a unique solution or not also can tells us if Ax=b has a solution or not.