Checking whether the result is positive definite or positive semi-definite with two methods Given, $$A = \begin{bmatrix}
1 &1  & 1\\ 
 1&1  & 1\\ 
 1&  1& 1
\end{bmatrix}.$$
I want to see if the matrix $A$ positive (negative)  (semi-) definite.
Using Method 1:
Define the quadratic form as $Q(x)=x'Ax$. 
Let $x \in \mathbb{R}^{3}$, with $x \neq 0$.
So, $Q(x)=x'Ax = \begin{bmatrix}
x_{1} &x_{2}  &x_{3} 
\end{bmatrix} \begin{bmatrix}
1 &1  & 1\\ 
 1&1  & 1\\ 
 1&  1& 1
\end{bmatrix} \begin{bmatrix}
x_{1}\\x_{2} 
\\x_{3} 
\end{bmatrix}$.
After multiplying out the matrices I am left with $$Q(x) = x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+2(x_{1}x_{2} + x_{1}x_{3}+x_{2}x_{3}).$$
So by Method 1, I get that $A$ is positive definite. 
Using Method 2:
I calculate all principle minors $A$ and if they're all positive, then the matrix is positive definite (learned recently from @hermes). 
So $|A_{1}| =1> 0$, $|A_{2}| = 0$, and $|A_{3}| = |A| = 0$.
So $A$ is positive semi-definite.
Which method am I making a mistake?

First is wrong. $Q(x)$ doesn't mean $A$ is positive definite. 
Moreover $rank(A)=1$. Since $A$ is not of full rank, it can not be positive definite.
