Let $v=(x,y)^T$ a vector of $R^2$ and the quadratic form $Q(x,y)=4x^2+2xy+4y^2$.Find the matrix representation $A$ of $Q(x,y)$.
What I know is that you can represent the quadratic form $Q(x,y)=ax^2+2bxy+cy^2$ as $Q(x,y) = x^TAx=\left[\begin{array}{cc} x & y \end{array}\right] \left[\begin{array}{cc} a & b \newline b & c \end{array}\right] \left[\begin{array}{cc} x \newline y\end{array}\right]$
Is $ A = \begin{bmatrix} a & b \newline b & c \end{bmatrix}$ the representation matrix? And if not ,what is the matrix?