That system is the same as:
which can be written
This is a homogeneous system, which means all the
constant terms are 0.
A homogeneous system always has solution (0,0,0) and
that is the only solution it can have it the matrix
of the coefficients is not singular.
Since we are told that x is not 0, we know that the
matrix of coeficients is singular and therefore the
determinant of coefficients must be 0. so we set the
determinant of coefficients = 0.
We evaluate the determinant (I assume you know how,
if you don't post again asking how.) We get:
-p + 12 = 0
-p = -12
p = 12
Edwin
