I should argument that this is $P^2 = P$ because the picture of P is in U.
can I argument that if I define this vector $v ∈ R^n and \ n ∈ N$
so $v = \left(\begin{matrix} a \\b \\c \end{matrix}\right), U = span(v)$
and $ P = \left(\begin{matrix} a^2 & ab & ac \\ab & b^2 & bc \\ac & bc & c^2 \end{matrix}\right)$
and if I calculate $ U * P = U$
Or is there a better way to show that?