What does it mean to have a determinant equal to zero? After looking in my book for a couple of hours, I'm still confused about what it means for a $(n\times n)$-matrix $A$ to have a determinant equal to zero, $\det(A)=0$.
I hope someone can explain this to me in plain English.

Take a 2 x 2 matrix, call it A, plot that in a coordinate system. 
A= [[2,1],[4,2]] . --> Numpy notation of a matrix
Following two vectors are written from A
x=[2,4]
y=[1,2]
If you plot that, you can see that they are in the same span. That means x and y vectors do not form an area. Hence, the det(A) is zero. Det refers to the area formed by the vectors. 
