\begin{tikzpicture}[scale=0.75]
  \draw [thick, black, ->] (0,0) -- (9,0)
  node [above, black] {$x$};

  \draw [thick, black, ->] (0,0) -- (0,7)
  node [right, black] {$y$};

  \draw [thick, blue, ->] (0,0) -- (1,3)
  node [right, black] {$x = \left[ \begin{array}{c}
          1 \\
          3
        \end{array} \right]$};

  \draw (0.5,6)
  node [right, black] {$A = \left[ \begin{array}{cc}
          1 & 2 \\
          2 & 1
        \end{array} \right]$};

  \onslide<3->{
    \draw [thick, blue, ->] (0,0) -- (7,5)
    node [right, black] {$Ax = \left[ \begin{array}{c}
            7 \\
            5
          \end{array} \right]$};
  }
  \foreach \x/\xtext in {1/1,2/2,3/3,4/4,5,5,6/6,7/7,8/8 }
    {
      \draw[shift={(\x,0)}] (0pt, 2pt) -- (0pt, -2pt);
    }
  \foreach \y/\ytext in {1/1,2/2,3/3,4/4,5,5,6/6}{
      \draw[shift={(0,\y)}] (2pt, 0pt) -- (-2pt, 0pt);
    }
\end{tikzpicture}