In this segment we are talking about some
theorems corresponding to eigenvalues and
eigenvectors and one of the theorems says
that if lambda_1-lambda_n are eigenvalues
of nxn [A] matrix so your squared matrix which
is nxn then you can find then you can find
det(A)= lambda_1 * lambda_2 *...*lambda_n
absolute value 
so in order to find the magnitude of the det(A)
all you have to do is you take all the eigenvalues
find the product of those eigenvalues and
you get the det(A) the magnitude of that which
can also be written as this: i is equal from
1 to n, lambda_i.
But you also now lets us make sense out of
one of the theorems that if one of the eigenvalues
is zero then the [A] matrix is not invertible
its singular it can not inverse can not be
found which makes sense because if one of
the eigenvalues is zero then the product of
all these is going to be zero in the spector
of what the other eigenvalues are then the
det the magnitude of the det(A) is going to
be zero which means the det(A) is going to
be zero which basically means that the [A]
matrix is singular so that s just another
way of proving that particular theorem but
lets take an example and see what we mean
by that so if somebody says im going to give
you an [A] matrix [A]=2, -3.5, 6, 3.5, 5,
2, 8,1, 8.5 and they are also telling that
im giving you the eigenvalues of this square
matrix lambda1= -1.547, lambda2= 12.33, lambda3=
4.711 can you find the magnitude of the determinant
and you got to say yes I can find the magnitude
of the determinant because I know that the
magnitude of the det(A) is nothing but det(A)=lambda1
* lambda2 * lambda3=(-1.54)(12.33)(4.711)
absolute value 
and this number turns out to be =89.88 so
that's the magnitude of the det(A) which basically
means that the det(A) is either -89.88 or
+ 89.88 but you are able to find the magnitude
of the det(A) which might be the most important
thing to find in most cases and that s the
end of this segment
